FBP 2021

15th International Conference on Free Boundary Problems: Theory and Applications

Berlin, Germany, September 13–17, 2021
Program Committee
Gui-Qiang G. ChenCharlie Elliott
Harald Garcke
Yoshikazu Giga
Michael Hintermüller
Ralf Kornhuber
Ricardo H. Nochetto
Elisabetta Rocca
José Francisco Rodrigues
James A. SethianHenrik Shahgholian
Halil Mete Soner

Organizing Committee
Carsten Gräser (FU Berlin)
Michael Hintermüller (WIAS
Berlin, HU Berlin, Chair)
Dietmar Hömberg (WIAS Berlin)
Ralf Kornhuber (FU Berlin)
Jürgen Sprekels (WIAS Berlin)
Barbara Wagner (TU Berlin)

Local Support Team
Amal Alphonse
Jo Andrea Brüggemann
Caroline Geiersbach
Olivier Huber
Axel Kröner
Hongying Pan
Patricia Rouland

Welcome Address
Welcome to the 15th International Conference on Free Boundary Problems: Theory
and Applications!
This edition of the conference is special in several respects. First and foremost,FBP 2021 has attracted an excellent group of plenary speakers, it offers a list ofminisymposia on very timely topics, and it has received very interesting contributed
presentations. This is clearly a sign that the community is very active and thriving.
On the other hand, FBP 2021 stands out of the conference series as it will
be held fully online for the first time ever, owing to the consequences of the
COVID pandemic. Needless to say that the local organizing team and the Berlin
mathematical community would have preferred an in-person meeting at HumboldtUniversität zu Berlin, as originally planned for 2020. Indeed, gathering a group of
esteemed colleagues at a place for intense scientific exchange is always rewarding
in many respects. In order to cope as best as possible with the challenges ofholding an international meeting online, the organizing team has tried to adjust
the schedule to the various time zones and employ electronic tools which admit
ad hoc discussions and personal encounters. With these measures in place andgiven our experience as a community with virtual meetings, the organizing team
as well as the program committee are confident that FBP 2021 will add anotherhighlight to this traditional conference series.
Overall, we are looking forward to about 150 invited and contributed talks and
12 invited plenary lectures. The electronically available conference book has been
designed to provide quick information and access to virtual presentation rooms.
Moreover, we hope that you will use it to select not only minisymposia sessions
that you find interesting to attend but also that you will peruse talks by our
excellent contributed speakers. Our warm gratitude goes to the minisymposia
organizers and speakers as well as the contributed speakers without whom thisconference could not exist.
We wish you all a pleasant and memorable FBP 2021, and a lot of exciting
mathematics!

2

Sponsors

FBP 2021 is Supported by3

Contents
Sponsors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Plenary Speakers and Minisymposia Organizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Biographies of Plenary Speakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Daily Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Plenary Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Parallel Sessions Abstracts Mon 09:50–11:50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Parallel Sessions Abstracts Mon 12:45–14:45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Parallel Sessions Abstracts Tue 09:50–11:50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Parallel Sessions Abstracts Tue 12:45–14:45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Parallel Sessions Abstracts Tue 17:05–19:05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Parallel Sessions Abstracts Wed 09:50–11:50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Parallel Sessions Abstracts Wed 12:45–14:45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Parallel Sessions Abstracts Wed 16:15–18:15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Parallel Sessions Abstracts Thu 09:50–11:50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Parallel Sessions Abstracts Thu 12:45–14:45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Parallel Sessions Abstracts Thu 16:15–18:15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Parallel Sessions Abstracts Fri 09:50–11:50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Parallel Sessions Abstracts Fri 12:45–14:45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Index of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4

Plenary Speakers and Minisymposia Organizers

Plenary Speakers and Minisymposia Organizers

Plenary speakers
S ö r e n B a rt e l s
U Freiburg

Qiang Du
Columbia U

X av i e r Ro s - O t o n
U ZurichA n d r e a B e rt o z z i
UCLA

Alessio Figalli
ETH Zurich

Ro b e rt S ay e
Lawrence Berkeley Lab

L i a B ro n s a r d
McMaster U

I r e n e Fo n s e c a
Carnegie Mellon U

Y o s h i h i ro T o n e g awa
Tokyo Institute of Technology

Antonin Chambolle
U Paris-Dauphine PSL

Barbara Niethammer
U BonnEnrique Zuazua
U Erlangen

Minisymposia
Nonlocal free boundary problems
J.-F. Rodrigues, E. Valdinoci

Free boundary problems related to Regularity of free boundaries
shapes and geometries
H. Shahgholian, M. Smit Vega Garcia
G. Buttazzo, E. Oudet

Phase field models
E. Rocca, V. Styles

Optimization and control of FBPs Numerical methods for geometric
PDEs
M. Hintermüller, M. Hinze
R. Nochetto, R. Nürnberg

Surface PDEs
C. Venkataraman, T. RannerFree boundary models in active Numerical methods for surface-bulk
matterproblems
L. Berlyand
E. Bänsch, A. Reusken

Interfaces in fluids
H. Abels, H. Garcke, M. WilkeFBP in the life sciences
L. Berlyand, A. Friedman

Free boundary problems for nonlinear hyperbolic/mixed-type PDEs
G.-Q. Chen

Stochastic free boundary problems Free boundary problems in cell bi- Asymptotic approaches to interface
A. Djurdjevac, B. Gess, G. Grün
ology
dynamics
C. Gräser, M. Röger
J. José López Velázquez, J. King
Geometric problems
Y. Giga, M. Novaga

UQ in free boundary problems
H. Harbrecht, M. D. Multerer

Geometric evolution of interfaces
and transition layers(contributed minisymposium)
P. Rybka, G. Wheeler

Biographies of Plenary Speakers

5

Biographies of Plenary Speakers

Sören Bartels (University of Freiburg) is an applied mathematician whose interests lie in the development and analysis ofapproximation schemes for PDEs with applications in material science and geometry. He is also the author of several books
related to numerical methods for PDEs.

Andrea Bertozzi (University of California, Los Angeles) is an applied mathematician with expertise in nonlinear partial differential
equations and fluid dynamics. She also works in the areas of geometric methods for image processing, crime modeling andanalysis, and swarming/cooperative dynamics. Bertozzi completed all her degrees in mathematics at Princeton. Since 2005 she
has served as Director of Applied Mathematics, overseeing the graduate and undergraduate research training programs at UCLA.
In May 2018 Bertozzi was elected to the US National Academy of Sciences. In July 2019 she was awarded SIAM’s Kleinman
Prize, which recognizes contributions that bridge the gap between high-level mathematics and engineering problems.

Lia Bronsard (McMaster University) is originally from Québec and did her undergraduate studies at the Université de Montréal,
graduating in 1983. She earned her PhD in 1988 from New York University under the supervision of Robert V. Kohn. After
short-term positions at Brown University, the Institute for Advanced Study, and Carnegie Mellon University, she moved to
McMaster University in 1992. She was president of the Canadian Mathematical Society for 2014–2016. Bronsard was a plenary
speaker at the SIAM Annual meeting in Boston in 2016, at the Mathematical Congress of the America in Montreal in 2017, andat the CMS Summer meeting in Charlottetown in 2018. She is on the editorial board of Nonlinear Analysis, Mathematics inScience and Industry, and the Canadian Applied Math Quarterly. In her research, she has used geometric flows to model theinterface dynamics of reaction–diffusion systems. Other topics in her research include pattern formation, grain boundaries, andvortices in superfluids. Bronsard was the 2010 winner of the Krieger–Nelson Prize. In 2018 the Canadian Mathematical Society
listed her in their inaugural class of fellows.

Antonin Chambolle (CNRS and Université de Paris-Dauphine PSL) is a CNRS research director at CEREMADE, Université deParis-Dauphine PSL (France). His research focuses on free boundaries or free discontinuity problems, variational methods inimage processing, variational brittle fracture theory in elasticity and continuous (convex) optimization.

Qiang Du (Columbia University) is the Fu Foundation Professor of Applied Mathematics at the Department of Applied Physics
and Applied Mathematics (APAM), Fu Foundation School of Engineering and Applied Science (SEAS), Columbia University.
He is also an affiliated with the Data Science Institute (DSI). He chaired the Applied Mathematics Program Committee from2014–2020 and served in DSI as a co-Chair of the Center for Foundations of Data Science from 2017–2019. Currently he also
serves as a co-chair of the Center for Computing Systems for Data-Driven Science.

Alessio Figalli (ETH Zürich) works in the theory of optimal transportation, elliptic PDEs, free boundaries, and functional
inequalities. He has also given several contributions to the theory of transport equations with rough vector-fields, Hamilton-Jacobi
equations, and random matrices. He received the Fields Medal in 2018.

Irene Fonseca (Carnegie Mellon University) received her Ph.D. degree in mathematics in 1985 from the University of Minnesota,
has been a faculty member in the Mellon College of Science since 1987 and is the director of the university’s Center for Nonlinear
Analysis. She has supervised 16 Ph.D. students and mentored 41 postdoctoral fellows. One of the world’s leading researchers in
the field of applied mathematics, Fonseca’s research lies at the interface of applied analysis with materials and imaging sciences.
In 2012, she became the second woman to be elected president of the Society for Industrial and Applied Mathematics (SIAM).
She is a Fellow of the American Mathematical Society (AMS) and of SIAM. She is a Grand Officer of the Military Order of SaintJames of the Sword (Grande Oficial da Ordem Militar de Sant’Iago da Espada, Portuguese Decoration). She received the Mellon
College of Science chair in 2003, in 2014 she was named University Professor, the highest distinction that can be bestowed on aprofessor at CMU, and in 2018 she was endowed the Kavčić–Moura chair in mathematics. Fonseca serves in 18 editorial boards,
including Advances in Calculus of Variations, Archive for Rational Mechanics and Analysis, ESAIM:COCV (SMAI), Journal of
Nonlinear Science, M3AS, and SIAM Journal on Mathematical Analysis. She is a member of several advisory and scientific boardsof research centers and institutes, including the IMA, she participates in international prize committees, and is in review andevaluation panels of multiple universities in the US and abroad.

Barbara Niethammer (University of Bonn) is a professor at the Hausdorff Center for Mathematics at the University of Bonn.
Her research interests are in applied mathematics and include the analysis of problems with multiple scales, dynamics in highdimensional dynamical systems and universal scaling behavior in models of mass aggregation and coarsening. Niethammer won
the Richard von Mises Prize of the Gesellschaft für Angewandte Mathematik und Mechanik in 2003 for her work on Ostwald
ripening, and the Whitehead Prize of the London Mathematical Society in 2011 "for her deep and rigorous contributions tomaterial science, especially on the Lifshitz–Slyozov–Wagner and Becker–Doering equations".

6

Biographies of Plenary Speakers

Xavier Ros-Oton (University of Barcelona) has made outstanding contributions to the analysis of various aspects of elliptic andparabolic PDEs, including free boundary problems. He has won numerous awards for his achievements by various societies/institutes
in Spain, including being chosen as the winner of the prestigious Premio Investigación Científica 2019 award (granted by the kingof Spain) for young Spanish mathematicians. He is a PI of a ERC Starting Grant where he was the youngest awardee amongst
all starting grants in 2018 across all the sciences. His collaborators include exemplary figures in the free boundary problem
community such as Luis Caffarelli.

Robert Saye (Lawrence Berkeley National Laboratory) is an applied mathematician in the Mathematics Group of the Computational
Research Division at the Lawrence Berkeley National Laboratory and is also affiliated with the Department of Mathematics of the
University of California at Berkeley. His research interests are in mathematical modelling and scientific computation, particularly
numerical methods for interfacial fluid dynamics, high-order accurate algorithms for implicitly defined geometry, and multi-scale
and multi-physics simulation.

Yoshihiro Tonegawa (Tokyo Institute of Technology) is an expert working in elliptic and parabolic PDEs as well as geometricmeasure theory and curvature flows.The quality of his work was recognised in 2010 when he won the Fukuhara Prize of theMathematical Society of Japan and once again in 2013 when he won the society’s Analysis Prize. He is also the author of a bookon Brakke’s mean curvature flow.

Enrique Zuazua (University of Erlangen–Nuremberg) is Chair Professor in Applied Analysis — Alexander von Humboldt
Professorship at the University of Erlangen–Nuremberg (FAU). He is also the Principal Investigator of the European ResearchCouncil (ERC) Advanced Grant “DyCon - Dynamic Control”, at the Chair of Computational Mathematics of Deusto Foundation in
Bilbao and Universidad Autónoma de Madrid (UAM). His domains of expertise in applied mathematics include partial differential
equations, control theory, numerical analysis, and data sciences. These subjects interrelate with the final to model, analyse,
compute, simulate, and finally contribute to the control and design of the most diverse natural phenomena and all fields of R & D.

A communication from Henrik Shahgholian
The free web-based platform called SciLag, accessible at https://scilag.net, provides tools for mathematicians to collaboratively build a dynamic and tractable database of open problems in mathematics, allowing researchers to announce, discover,and discuss open problems stemming from their research. A few examples of our current problems are:
PDE: https://www.scilag.net/problem/P-180630.2
Group Theory: https://www.scilag.net/problem/P-180619.3
Probability: https://www.scilag.net/problem/P-181120.2
Diff. Geometry: https://www.scilag.net/problem/P-180904.1
Combinatorics/PDE: https://www.scilag.net/problem/P-181023.1
Combinatorics: https://www.scilag.net/problem/P-181012.1
The following pdf fileillustrates a Scilag-page for registered members.

Daily Overview

Daily Overview

Monday13.09.2021

08:45–09:00: Opening

Lecture hall

09:00–09:45: Plenary
Discretizations of the total variation for singular functions

Lecture hall
page 12Antonin Chambolle

09:50–11:50: Parallel Sessions
Interfaces in fluids (Part I), H. Abels, H. Garcke, M. Wilke
Christina Lienstromberg
Marius Tucsnak

Elisabetta Rocca

Room 1
Piotr B. Mucha

page 18

Optimization and control of FBPs (Part I), M. Hintermüller, M. Hinze
Christian Kahle

Tobias Keil

Kei Fong Lam

Room 2
page 19

Dirk Peschka

Room 3page 19

Numerical methods for surface-bulk problems (Part I), A. Reusken, E. Bänsch
Markus Gahn

André Massing [canceled]

12:45–14:45: Parallel Sessions
Free boundary problems related to shapes and geometries, E. Oudet, G. Buttazzo
Giuseppe Buttazzo

Edouard Oudet

Bozhidar Velichkov

Phase field models (Part I), E. Rocca, V. Styles
Klaus Deckelnick
Maurizio Grasselli

Pierluigi Colli

Room 1
page 20
Room 2

Michael Hinze

page 20

15:00–15:45: Plenary
Phase transitions in heterogeneous media: equilibria and geometric flows
Irene Fonseca

Lecture hall
page 12

16:15–17:00: Plenary
Higher-Order Numerics for Interfacial Fluid Dynamics
Robert Saye

Lecture hall
page 137

8

Daily Overview

Tuesday

14.09.2021

09:00–09:45: Plenary
Generalized mean curvature flow

Lecture hall
page 13

Yoshihiro Tonegawa

09:50–11:50: Parallel Sessions
Geometric problems (Part I), M. Novaga, Y. Giga
Miyuki Koiso

Tatsuya Miura

Enrico Valdinoci

Interfaces in fluids (Part II), H. Abels, H. Garcke, M. Wilke
Dieter Bothe
Hao Wu [canceled]Philippe Laurençot

Room 1
page 21
Room 2

Hans Knüpfer

page 21

Free boundary problems for nonlinear hyperbolic/mixed-type PDEs (Part I), G.-Q. Chen

Room 3Myoungjean Bae
Wei Xiang

page 22

Hyangdong Park

Tao Wang

12:45–14:45: Parallel Sessions
Phase field models (Part II), E. Rocca, V. Styles
Luca Scarpa
Harald Garcke

Björn Stinner

Room 1
Marita Thomas

page 23

UQ in free boundary problems, H. Harbrecht, M. D. Multerer
Caroline Geiersbach
Helmut Harbrecht

Alexey Chernov

Room 2
Nick Wulbusch

page 24

15:00–15:45: Plenary
Patterns in tri-block copolymers: droplets, double-bubbles and core-shells

Lecture hall
page 14

Lia Bronsard

17:05–19:05: Parallel Sessions
Numerical methods for geometric PDEs (Part I), R. Nochetto, R. Nürnberg
Andrea Bonito
Sören Bartels

Wenbo Li

Room 1
Shawn Walker

page 25

Contributed session (Part I)
Diogo Caetano
Makoto Okumura

Room 2
Lars von Wolff

Alice Marveggio

page 26

Contributed session (Part II)
Dominik Edelmann
Xinyue Zhao

Room 3
Kota KumazakiMartin Weiser

page 27

Contributed session (Part III)
Nino Khatiashvili
Kyung Ha

Room 4
Vladislav Pukhnachev

Athanasios Stylianou

page 28

Daily Overview

Wednesday

15.09.2021

09:00–09:45: Plenary
Simulation of Free Boundary Problems in the Nonlinear Bending of Elastic Rods and Plates
Sören Bartels

Lecture hall
page 14

09:50–11:50: Parallel Sessions
Surface PDEs (Part I), C. Venkataraman, T. RannerPhilip Brandner

Argyrios Petras

Marino Arroyo

Nonlocal free boundary problems (Part I), E. Valdinoci, J.-F. Rodrigues
Alexander Nazarov
Juan Luis Vázquez

Room 2

Aram Karakhanyan

Xavier Fernández-Realpage 29

Stochastic free boundary problems (Part I), A. Djurdjevac, B. Gess, G. Grün
Lubomir Banas
Sebastian Hensel

Room 3

Nicolas Dirr

Hubertus Grillmeier

page 30

Geometric problems (Part II), M. Novaga, Y. Giga
Paola Pozzi
Mathias Wilke

Room 1
page 29

Room 4

Lucia Scardia

Ulisse Stefanelli

page 31

12:45–14:45: Parallel Sessions
Regularity of free boundaries (Part I), H. Shahgholian, M. Smit Vega Garcia
Jinwan Park
Simon Eberle

Room 1Sunghan Kim

Nicola Soave

page 32

Numerical methods for surface-bulk problems (Part II), A. Reusken, E. Bänsch
Stefan Metzger
Alfred Schmidt

Robert Nürnberg

Room 2
Thomas Ranner

page 32

Optimization and control of FBPs (Part II), M. Hintermüller, M. Hinze
René Pinnau [canceled]Björn Baran

Dmytro Strelnikov

Room 3Patrik Knopf

page 33

Interfaces in fluids (Part III), H. Abels, H. Garcke, M. Wilke
Andrea Giorgini

Ian Tice

Maurizio Grasselli

Room 4page 34

15:00–15:45: Plenary
Nonlocal variational geometric problems with free boundary

Lecture hall
page 15

Qiang Du

16:15–18:15: Parallel Sessions
Numerical methods for geometric PDEs (Part II), R. Nochetto, R. Nürnberg
Antonin Chambolle
Martin Rumpf

Klaus Deckelnick

Room 1
Hanne Hardering

page 35

Free boundary models in active matter, L. Berlyand
Leonid Berlyand
Carles Blanch-Mercader

Ricard Alert

Room 2
Jaume Casademunt

page 35

Regularity of free boundaries (Part II), H. Shahgholian, M. Smit Vega Garcia
Mark Allen
Murat Akman

Dennis Kriventsov

Room 3
Edgard Pimentel

page 369

10

Daily Overview

Thursday16.09.2021

09:00–09:45: Plenary
An obstacle problem for cell polarization

Lecture hall
page 15

Barbara Niethammer

09:50–11:50: Parallel Sessions
Asymptotic approaches to interface dynamics (Part I), J. José López Velázquez, J. King

Room 1

John Ward
Scott McCue

page 37

Amrita Ghosh

Diego Alonso Oran

Stochastic free boundary problems (Part II), A. Djurdjevac, B. Gess, G. Grün
Ana Djurdjevac

Room 2
page 38

Free boundary problems for nonlinear hyperbolic/mixed-type PDEs (Part II), G.-Q. Chen

Room 1

Mikhail Feldman
Steve Shkoller

page 39

Peter Nejjar

Benjamin Seeger

12:45–14:45: Parallel Sessions
Paolo Secchi

Dehua Wang

Free boundary problems in cell biology (Part I), C. Gräser, M. Röger
Helmut Abels
Anna Logioti

Martin Burger

Room 2
Luca Lussardi

page 39

Nonlocal free boundary problems (Part II), E. Valdinoci, J.-F. Rodrigues
Lisa Santos
Harbir Antil

Eduardo Teixeira

Room 3Catharine W.K. Lo

page 40

15:00–15:45: Plenary
Generic regularity in obstacle problems

Lecture hall
page 16

Alessio Figalli

16:15–18:15: Parallel Sessions
FBP in the life sciences, A. Friedman, L. Berlyand
Avner Friedman
Tim Laux

Bei HuRoom 2Adrian Lam

page 41

Geometric evolution of interfaces and transition layers (Part I), G. Wheeler, P. Rybka

Room 1Marco Morandotti
Mikołaj Sierżęga

page 42

Danielle Hilhorst

Katarzyna Ryszewska

Contributed session (Part IV)
Rolf Krause
Lucas Daniel Wittwer

Room 3Irina Denisova

Sebastian Alandpage 42

Contributed session (Part V)
Guozhi Dong

Vladimir Vasilyev

Seongmin Jeon

Room 4page 43

18:20–19:05: Plenary
Energy Minimizing Surface Tension Configurations for Microparticles
Andrea Bertozzi

Lecture hall
page 16

Daily Overview

Friday17.09.2021

09:00–09:45: Plenary
Inverse design for conservation laws and Hamilton-Jacobi equations

Lecture hall
page 17

Enrique Zuazua

09:50–11:50: Parallel Sessions
Geometric evolution of interfaces and transition layers (Part II), G. Wheeler, P. Rybka

Room 1Glen Wheeler
Piotr Rybka

page 44

James McCoy

Simon Blatt

Contributed session (Part VI)
Enrico Valdinoci
Yvonne Stokes

Room 2
Subas Acharya

Xin Liu

page 44

12:45–14:45: Parallel Sessions
Free boundary problems in cell biology (Part II), C. Gräser, M. Röger
Chandrasekhar Venkataraman

Philip Herbert

Diane Peurichard

Surface PDEs (Part II), C. Venkataraman, T. Ranner
Axel Voigt
Matthias Röger

Paola Pozzi

Room 2
Balázs Kovács

page 45

Asymptotic approaches to interface dynamics (Part II), J. José López Velázquez, J. King
Jonas Jansen

Room 1
page 45

Mark Blyth

Linda Cummings

Room 3page 46

15:00–15:45: Plenary
The size of the singular set in the Stefan problem
Xavier Ros-Oton

15:45–16:00: Closing

Lecture hall
page 17
Lecture hall

11

12

Plenary Talks

Plenary Talks
Plenary Talk

Plenary Talk

Mon 09:00–09:45

Mon 15:00–15:45

Antonin Chambolle, CNRS and CEREMADE, Université
Paris-Dauphine, PSL, France
Discretizations of the total variation for singular functions

Irene Fonseca, Carnegie Mellon University
Phase transitions in heterogeneous media: equilibria
and geometric flows

The total variation, which is used as a regularizer in inverse
problems in imaging or to compute minimal surfaces, is thesimplest example of a convex functional whose minimizers are
typically discontinuous. This raises interesting numerical issues,
as there are many ways to discretize it, most of which withdrawbacks such as a loss of isotropy or important numerical
diffusion. In this talk I will review some recent results (obtainedin collaboration with C. Caillaud and T. Pock (TU Graz)) about
the discretization errors for this functional, and introduce afamily of consistent discretizations which can be improved bya learning strategy, yielding sharper interfaces or “nicer” image
denoising.

A variational model in the context of the gradient theory
for fluid-fluid phase transitions with small scale heterogeneities
is studied. In the case where the scale of the small homogeneities is of the same order of the scale governing the phasetransition, the interaction between homogenization and thephase transitions process leads to an anisotropic interfacial
energy. The underlying gradient flow provides unconditional
convergence results for an Allen-Cahn type bi-stable reaction
diffusion equation in a periodic medium. curvature, is obtained.
This is joint work with Riccardo Cristoferi (Radboud University,
The Netherlands), Adrian Hagerty, Cristina Popovici, Rustum
Choksi (McGill), Jessica Lin (McGill), and Raghavendra Venkatraman (CMU).

Plenary Talks

Plenary Talk

13

Plenary Talk

Mon 16:15–17:00

Tue 09:00–09:45

Robert Saye, Lawrence Berkeley National Laboratory
Higher-Order Numerics for Interfacial Fluid Dynamics

Yoshihiro Tonegawa, Tokyo Institute of Technology
Generalized mean curvature flow

Surface, boundary, and interface motion play a pivotal rolein a wide range of fluid dynamics problems. When modellingthese problems computationally, a careful and precise treatment of the interface is often necessary - boundary layers canstrikingly affect interface motion, while small-scale features insurface geometry can affect fluid dynamics far afield. In thistalk, we discuss some of our work on developing higher-ordernumerical methods for interfacial fluid dynamics, including
implicit mesh discontinuous Galerkin (DG) methods which
utilize level set methods to create implicitly-defined meshes
capable of imposing or capturing interfacial jump conditions
with high-order accuracy. Highlighted topics include high-order
quadrature algorithms for multi-component implicitly definedgeometry, and fast multigrid solvers for DG discretizationsof elliptic interface/Stokes problems. We also present some
applications, including: high-Reynolds number soap bubble
oscillations; multi-scale models of membrane rearrangement,
drainage and rupture in foam dynamics; vortex shedding dynamics created by intricate Plateau-Rayleigh instabilities; andmodeling rotary bell atomization in industrial spray painting
processes.

I will discuss a time-global existence theorem of generalized
mean curvature flow which can move with singularities suchas triple junctions and which goes through various topological changes as it evolves. It is a so-called Brakke flow but it
additionally satisfies other characterizations such as BV characterization. I plan to give a sketch on how to construct thesolution and what it satisfies.

14

Plenary Talks

Plenary Talk

Plenary Talk

Tue 15:00–15:45

Wed 09:00–09:45

Lia Bronsard, McMaster University
Patterns in tri-block copolymers: droplets, doublebubbles and core-shells

Sören Bartels, University of Freiburg
Simulation of Free Boundary Problems in the Nonlinear Bending of Elastic Rods and Plates

We study the Nakazawa-Ohta ternary inhibitory system,
which describes domain morphologies in a triblock copolymer
as a nonlocal isoperimetric problem for three interacting phasedomains. The free energy consists of two parts: the local
interface energy measures the total perimeter of the phaseboundaries, while a longer-range Coulomb interaction energy
reflects the connectivity of the polymer chains and promotes
splitting into micro-domains. We consider global minimizers on
the two-dimensional torus, in a limit in which two of the species
have vanishingly small mass but the interaction strength iscorrespondingly large. In this limit there is splitting of themasses, and each vanishing component rescales to a minimizerof an isoperimetric problem for clusters in 2D. Depending on therelative strengths of the coefficients of the interaction terms we
may see different structures for the global minimizers, ranging
from a lattice of isolated simple droplets of each minority
species to double-bubbles or core-shells. This represents workwith S. Alama, X. Lu, and C. Wang.

The mathematical description of large bending deformationsof thin elastic rods and plates leads to fourth order problems
with nonlinear pointwise constraints that give rise to various freeboundary phenomena. The free boundary may separate regionsof trivial and large deformations, describe the contact zone in
the presence of an obstacle, or be related to the occurrence ofself-contact. We devise and analyse numerical methods thatare capable of reliably capturing these effects under minimal
regularity assumptions and which allow us to experimentally
study topological transitions of free boundaries.

Plenary Talks

Plenary Talk

Plenary Talk

Wed 15:00–15:45

Thu 09:00–09:45

Qiang Du, Columbia University
Nonlocal variational geometric problems with freeboundary

Barbara Niethammer, University of Bonn
An obstacle problem for cell polarization

We will discuss a couple of variational problems in geometry with free boundary. These problems are motivated fromapplications in biology and chemistry and all involve nonlocal
contributions in the energy functionals. We will study bothanalytical and numerical aspects of the variational problems
and present algorithms that can be used to explore the energy
landscape.

15

We investigate a model for cell polarization under external
stimulus where a diffusion equation in the inner cell is coupled
to reaction diffusion equations on the cell membrane. In certain
scaling limits we rigorously derive generalized obstacle typeproblems. For these limit systems we prove global stability ofsteady states and characterize the parameter regime for the
onset of polarization.

16

Plenary Talks

Plenary Talk

Plenary Talk

Thu 15:00–15:45

Thu 18:20–19:05

Alessio Figalli, ETH-Bereich Hochschulen
Generic regularity in obstacle problems

Andrea Bertozzi, UCLA math department
Energy Minimizing Surface Tension Configurationsfor Microparticles

The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held
fixed and which is constrained to lie above a given obstacle.
By classical results of Caffarelli, the free boundary is C ∞ outside a set of singular points. Explicit examples show that the
singular set could be in general (n − 1)-dimensional — that is,
as large as the regular set. In a recent paper with Ros-Oton
and Serra we show that, generically, the singular set has zeroHn−4 measure (in particular, it has codimension 3 inside thefree boundary), solving a conjecture of Schaeffer in dimension
n ≤ 4. The aim of this talk is to give an overview of theseresults.

Drop-Carrier Particles (DCPs) are solid microparticles designed to capture uniform microscale drops of a target solution
without using costly microfluidic equipment and techniques.
DCPs are useful for automated and high-throughput biologicalassays and reactions, as well as single cell analyses. DCPs enable templated uniform-sized droplets due to energy minima
achieved for the free boundary problem of the interface between immiscible liquids such as oil and water. Each DCP has
an energy-volume graph a finite volume acheiving the lowest
energy state. This allows for multiple DCPs to exchange fluidso that a system of particles has a lowest energy state in which
all but one DCP contain the same uniform volume. We compare the theoretical prediction for the volume distribution tomacroscale experiments of pairwise droplet splitting, with good
agreement. This leads to a statistical theory for the numberof pairwise interactions of DCPs needed to reach a uniform
volume distribution. Heterogeneous mixtures of DCPs withdifferent sized particles require fewer interactions to reach aminimum energy distribution for the system. We present ideas
for the optimization of the DCP geometry for minimal required
target solution and uniformity in droplet volume.

Plenary Talks

Plenary Talk

17

Plenary Talk

Fri 09:00–09:45

Fri 15:00–15:45

Enrique Zuazua, Friedrich-Alexander-Universität ErlangenNürnberg
Inverse design for conservation laws and HamiltonJacobi equations

Xavier Ros-Oton, ICREA & Universitat de Barcelona
The size of the singular set in the Stefan problem

We discuss the problem of inverse design, or time inversion,for scalar conservation laws and Hamilton-Jacobi equations.
The presence of singularities in the forward evolution is anobstruction for backward uniqueness and the unilateral bounds
generated by the forward dynamics establishe thresholds on
the set of reachable data. In this lecture we shall present ourrecent works in collaboration with Thibault Liard and Carlos
Esteve, characterising the set of reachable states, identifying
the multiplicity of initial data leading to a final target, and thedetermining the role of backward entropy or viscous solutions.
We also develop numerical algorithms allowing to reconstruct
the set of inversions and present some numerical experiments.

The Stefan problem, dating back to the XIXth century, isprobably the most classical and important free boundary problem. The regularity of free boundaries in the Stefan problem
was developed in the groundbreaking paper (Caffarelli, Acta
Math. 1977). The main result therein establishes that the freeboundary is C ∞ in space and time, outside a certain set of
singular points. The fine understanding of singularities is ofcentral importance in a number of areas related to nonlinear
PDEs and Geometric Analysis. In particular, a major questionin such context is to establish estimates for the size of thesingular set. The goal of this talk is to present some new resultsin this direction for the Stefan problem in R3 . This is a joint
work with A. Figalli and J. Serra.

18

Parallel Sessions Abstracts Mon 09:50–11:50

Mon 09:50–11:50

Mon 09:50–11:50
Minisymposium
Mon 09:50–11:50 Room 1

Interfaces in fluids (Part I)
Organizers: H. Abels, H. Garcke, M. Wilke

Christina Lienstromberg, University of BonnAnalysis of non-Newtonian thin-film equations
I will offer an insight into mathematical models describing the
dynamic behavior of non-Newtonian thin films. The resulting
PDEs are in general nonlinear, degenerate, of fourth order, andwith a possibly “weak” dependence of the coefficients. I will
discuss recent results on such an evolution equation for theinterface separating two viscous immiscible fluids, confined
between two concentric cylinders rotating at a small relative
velocity. In this so-called Taylor-Couette setting, two competing
effects drive the dynamics of the interface - the surface tension
and the shear stresses induced by the rotation of the cylinders.
When the two effects are comparable, solutions behave, forlarge times, as in the Newtonian regime. For the regime inwhich surface tension effects dominate the stresses inducedby the rotating cylinders, we prove local existence of positive
weak solutions for both shear-thinning and shear-thickening
fluids. In the case of a shear-thickening fluid, one observes
that interfaces which are initially close to a circle converge
to a circle in finite time. The talk is based on a joint workwith Tania Pernas-Castaño and Juan Velázquez: https://arxiv.
org/abs/2012.10734.

Elisabetta Rocca, University of Pavia
A phase-field prostate cancer growth with chemotherapy and antiangiogenic therapy effects
Here, we present a mathematical model of prostate cancer
growth and chemotherapy recently introduced in collaboration with P. Colli, H. Gomez, G. Lorenzo, G. Marinoschi, an
A. Reali. We use the phase-field method to describe tumor
growth, which we assume to be driven by a generic nutrient
following reaction-diffusion dynamics. Cytotoxic chemotherapy
is included as a term downregulating tumor net proliferation,
while antiangiogenic therapy is modeled as a reduction in intratumoral nutrient supply. An additional equation couples
the tumor phase field with the production of prostate-specic
antigen. We prove the well-posedness of our model and we run
a series of simulations leveraging an isogeometric method to
explore the effects of cytotoxic and antiangiogenic therapies.

Piotr B. Mucha, University of Warsaw
Free boundary problems in viewpoint of DaPratoGrisvard theorem
I plan to talk about an approach to the free boundary problems in the special functional setting. We aim at showing
stability in time, hence generally we are required to have information in the L1 in time. Thanks to the abstract approachbased on the classical DaPrato-Grisvard theorem, we are able
to reproduce the estimate for a linearization in the L1 (0, ∞; X)
spaces, here X is a real interpolation space given in terms of
Besov framework. The talk is based on joint result with R.
Danchin, M. Hieber, P. Tolksdorf.

Marius Tucsnak, University of BordeauxLarge time behavior in some fluid-interaction problems
We consider several systems modelling the motion of rigid
bodies in a viscous fluid. We discuss the long time behaviorof solutions in terms of the fluid properties (incompressible
or compressible) and on the geometric setting (bounded or
unbounded domains in one or three space dimensions. The
focus is on the adiabatic piston problem in one space dimension(compressible case) and on the large time behavior of a solid
moving in an unbounded three dimensional incompressible
viscous fluid.

19

Minisymposium

Minisymposium
Mon 09:50–11:50 Room 2

Mon 09:50–11:50 Room 3

Optimization and control of FBPs (Part I)

Numerical methods for surface-bulk problems (Part I)

Organizers: M. Hintermüller, M. Hinze

Organizers: A. Reusken, E. Bänsch

Christian Kahle, Universität Koblenz-Landau
Optimal control of sliding droplets using the contact
angle

Markus Gahn, University of Heidelberg - Interdisciplinary
Center for Scientific Computing (IWR)
A mixed finite element method for coupled bulksurface problems including Wentzell-boundary conditions

We present results on optimal control of sliding droplets.
Here the contact angle between droplet and solid serves as acontrol variable. The fluid is modeled by a thermodynamicallyconsistent diffuse interface model with a suitable contact line
model. In earlier work [H. Bonart, C. Kahle, J.-U. Repke,
JCP 399 (2019)] we compared different time discretization
schemes for this model that mimics the energy behaviour ofthe continuous model. We now employ a particular scheme toderive existence of optimal controls for a time discrete optimal
control problem and also first order neccessary conditions. As
controls we consider finite dimensional controls for the contact
angle distribution. We test our approach by driving a droplet
up an inclined plate.

Tobias Keil, Weierstrass Institute
Optimal control of a coupled Cahn–Hilliard–Navier–Stokes system with variable fluid densities
This talk is concerned with the optimal control of two immiscible fluids. For the mathematical formulation a coupledCahn–Hilliard–Navier–Stokes system is used which involves
a variational inequality of 4th order. We discuss the differentiability properties of the control-to-state operator and thecorresponding stationarity concepts for the control problem.
Strong stationarity conditions are presented and a numericalsolution algorithm based on a bundle-free implicit programming approach is provided which terminates at an at least
C-stationary point which, in the best case, is even strongly
stationary.

Kei Fong Lam, Hong Kong Baptist University
Consistency of a phase field regularisation for an
inverse problem governed by a quasilinear Maxwell
system
We tackle an inverse problem of reconstructing a discontinuous coefficient in quasilinear H(curl) magnetostatic equations from measurements in a subdomain. To overcome theill-posedness of the inverse problem, we investigate two regularisations posed as constrained minimisation problems. The first
involves perimeter penalisation and the second involves phasefield regularisation. Existence of minimisers and consistency as
the penalisation parameters tending to zero are discussed. We
show under ideal situations a relation between parameters thatallows one to obtain a solution to the inverse problem fromthe phase field solutions, and then we investigate the sharp
interface limit of the first order optimality conditions of thephase field problem. This is joint work with Irwin Yousept.

In this talk we introduce and analyze a mixed finite-element
approach for an elliptic coupled bulk-surface problem with
Wentzell-boundary condition of second order. Such kind ofmodels can be obtained by dimension reduction and play animportant role in many applications for example in the medical
sciences. The model is formulated on a domain with a curvedsmooth boundary and we introduce a mixed formulation that isequivalent to the usual weak formulation. Furthermore, we derive optimal a priori error estimates between the exact solution
and the finite-element approximation. To this end the curved
domain is approximated by a polyhedral domain introducing
an additional geometrical error that has to be bounded.

André Massing, Norwegian University of Science and Technology
High order cut finite element methods for coupledbulk surface problems [canceled]
In this talk we present a unified framework for the formulationof unfitted finite element methods for elliptic and hyperbolic
problems. Both continuous and discontinuous Galerkin methods
are considered. The resulting framework allows for the unified
numerical treatment of a wide range of problems, including
boundary and interface problems as well as surface and mixeddimensional, coupled surface-bulk and interface-bulk problems.
In the second part of the talk, we discuss how to combine theframework with high-order time-stepping methods to discretize
coupled surface-bulk problems on moving domains.

Dirk Peschka, Weierstrass-Institut für Angewandte Analysis und Stochastik
Dynamic contact and their numerical discretization
for gradient systems
In this talk we will discuss an energy-based framework for freeboundary problems with dynamic contact angle and investigate
the numerical discretization of such nonlinear PDE problems.
Firstly, the mathematical structure of the gradient flow and theresulting weak formulation of the problem will be described.
Then, we present the time discretization of the PDE system.
Finally, different relevant applications and solutions will bepresented.

Mon 09:50–11:50

Parallel Sessions Abstracts Mon 09:50–11:50

20

Parallel Sessions Abstracts Mon 12:45–14:45

Mon 12:45–14:45
Minisymposium

Minisymposium
Mon 12:45–14:45

Mon 12:45–14:45 Room 1

Mon 12:45–14:45 Room 2Free boundary problems related to shapes and geometries

Phase field models (Part I)

Organizers: E. Oudet, G. Buttazzo

Giuseppe Buttazzo, University of Pisa
Upper and lower bounds for some shape functionals
The relations between two quantities related to the Laplace
operator are considered. In particular, taking as a model theheat diffusion, governed by the heat equation, we aim to study
the relations between the average temperature of a heatedbody and the temperature decay rate of the body in absenceof heat sources. The quantities above are expressed by theso-called “torsional rigidity” and by the principal eigenvalue ofthe Laplace operator. The relations above are studied in theclasses of general domains, convex domains, and domains witha small thickness. This allows to obtain a detailed descriptionof the Blasche-Santaló diagram of the two quantities. Several
open questions are discussed, in particular when the Laplacianis replaced by the p-Laplacian.

Edouard Oudet, Université Grenoble Alpes
Metric Optimization in Spectral geometry
The results of this talk on recent numerical aspects of metric
optimization have been obtained in collaboration with Chiu-Yen
Kao and Braxton Osting. The first part of the talk is dedicatedto Nash’s isometric embedding theorem for surfaces. We recall
the impressive results obtained by HEVEA’s project for the flat
torus (V. Borrelli, F. Lazarus, B. Thibert et al.) and illustrate
how spectral formulation may lead to a new intrinsic approach
which are not related to Gromov’s construction. Following
the theoretical results of Fraser and Schoen, we describe ina second part a numerical approach to approximate minimal
surfaces in the ball that is surfaces (i) contained in the ball (ii)that have zero mean curvature and (ii) meet the boundary of
the ball orthogonally.

Bozhidar Velichkov, University of Naples Federico II
Regularity of the optimal sets for the second eigenvalue of the Dirichlet Laplacian
We prove a regularity theorem for the sets Ω that minimise
the functional λ2 (Ω) + |Ω| among all open sets contained ina given smooth domain D ⊂ Rd ; λ2 (Ω) being the second
eigenvalue of the Laplacian with Dirichlet boundary conditionson ∂Ω, and |Ω| the Lebesgue measure of Ω. Precisely, we provethat Ω is equivalent to the disjoint union A ∪ B, where theboundaries of the sets A and B are C 1,α regular manifolds up
to a closed singular set, which is empty in dimension d ≤ 4
and has Hausdorff dimension at most d − 5, when d ≥ 5. Thisis a joint work with Dario Mazzoleni (University of Brescia)
and Baptiste Trey (University of Grenoble Alpes).

Organizers: E. Rocca, V. Styles

Klaus Deckelnick, Otto-von-Guericke-Universität Magdeburg
A practical phase field method for an elliptic surface
PDE
We consider a diffuse interface approach for solving an elliptic
PDE on a given closed hypersurface. The method is based on a(bulk) finite element scheme employing numerical quadrature
for the phase field function and hence is very easy to implementcompared to other approaches. We estimate the error in natural
norms in terms of the spatial grid size, the interface width andthe order of the underlying quadrature rule. Numerical test
calculations are presented which confirm the form of the error
bounds. This is joint work with John W. Barrett and Vanessa
Styles.

Pierluigi Colli, University of Pavia
Optimal control problems with deep quench approachand sparsity for phase field tumor growth models
The talk reports on some recent results obtained in collaboration with Andrea Signori and Juergen Sprekels. A distributed
optimal control problem is considered for a tumor growth modelof Cahn–Hilliard type including chemotaxis. The evolution of
the tumor fraction is governed by a pointwise inclusion involving the subdifferential of a double obstacle potential. The
control and state variables are nonlinearly coupled and the costfunctional contains a nondifferentiable term like the L1 -normin order to include sparsity effects. To face the difficulties in
the analysis, the so-called “deep quench approach” is employedso that the convex part of the double obstacle potential isapproximated by logarithmic functions from the interior of thedomain. This approximation is used to derive first-order optimality conditions also for the double obstacle case, by obtaininga variational inequality in terms of the associated adjoint statevariables. Finally, if time permits sparsity results for the optimal
controls are discussed.

Michael Hinze, Universität Koblenz-Landau
Shape and topology optimization in fluids using phasefield models
We consider a phase field approach to shape and topology
optimization in fluid flow. The mathematical modeling leads
to a PDE constrained optimization problem with control in
the coefficients where the control enters as phase field in theDarcy term of the Navier–Stokes model. We prove existenceof solutions and present a numerical realization based on thefinite element method. We illustrate the performance of ourapproach with some numerical examples.

Maurizio Grasselli, Politecnico di Milano
Conserved Allen-Cahn-Navier–Stokes systems
I intend to present some results on a model of phase separation in (incompressible) liquids proposed by M.-H. Giga,
A. Kirshtein, and C. Liu in 2018. This model consists of theNavier–Stokes equations coupled with the Allen-Cahn equation
and accounts for a variable density which may depend on thephase field. I shall focus on the conserved Allen-Cahn equation
with logarithmic potential. These results have been obtained
jointly with A. Giorgini (Indiana University, USA) and H. Wu(Fudan University, PRC).

Parallel Sessions Abstracts Tue 09:50–11:50

21

Tue 09:50–11:50
Tue 09:50–11:50 Room 2

Geometric problems (Part I)

Interfaces in fluids (Part II)

Organizers: M. Novaga, Y. Giga

Organizers: H. Abels, H. Garcke, M. Wilke

Miyuki Koiso, Kyushu University
Stable anisotropic capillary hypersurfaces in a wedge
and application to partially-crystalline variational
problems

Dieter Bothe, TU Darmstadt
On the velocity jump discontinuity for bubbles risingin a viscoelastic fluid

We study surfaces with constant anisotropic mean curvature
in a wedge and with free boundary on the boundary of thewedge in the three-dimensional euclidean space, which are
critical points of “the anisotropic surface energy and the wettingenergy” for variations preserving the enclosed volume. We showa uniqueness result for local minimizers of the total energy. The
results are generalized to hypersurfaces in higher dimensional
spaces. Moreover, the method is applied to the uniquenessproblem for stable solutions of partially-crystalline variational
problems for piecewise smooth hypersurfaces.

Tatsuya Miura, Tokyo Institute of Technology
Variational analysis of self-intersecting elastic curves
In this talk we study variational problems involving bending
energy for closed curves in Euclidean space under constraints
on self-intersections. We obtain optimal configurations, someof which are nonclassical shapes, and discuss applications andconnections to elastic flows, elastic networks, and elastic knots.

Enrico Valdinoci, University of Western Australia(Non)local phase coexistence models
We will discuss classical and recent results concerning the
Allen-Cahn equation and its long-range counterpart, especiallyin relation to its limit interfaces provided by (possibly nonlocal)
minimal surfaces.

It is well-known that bubbles rising in viscoelastic liquids
may exhibit a jump discontinuity of the rise velocity as a
critical bubble volume is exceeded. This phenomenon has been
extensively investigated in the literature, both by means ofexperiments as well as numerical simulations. The occurrenceof the velocity jump seems to be associated with a change of the
bubble shape under formation of a pointed tip at the rear andto the appearance of a so-called negative wake with the liquid
velocity behind the bubble pointing in the opposite direction
to that in viscous Newtonian fluids. We revisit this topic,
reporting in particular our findings from a local conformation
tensor analysis, which is able to explain a true discontinuity
in the terminal bubble rise velocity. This is joint work with G.
Brenn (TU Graz) and M. Niethammer (TU Darmstadt).

Philippe Laurençot, University of Toulouse
Some Properties of the thin film Muskat problem
The thin film Muskat describes the space-time evolution of
the heights of two fluid layers with different viscosities anddensities and is a second-order degenerate parabolic system featuring a full diffusion matrix. Some properties of this system will
be reviewed, mostly in one space dimension, including existenceof non-negative weak solutions, finite speed of propagation,
time-independent estimates, and large time behavior. The connection with the porous medium equation will be discussed aswell. Joint work with Bogdan-Vasile Matioc (Regensburg).

Hans Knüpfer, Universität Heidelberg
Self-similar lifting and persistent touch-down point
solutions in the thin-film equation
In the talk I discuss the appearance of self-similar blowup solutions for thin-film equations with different mobility
exponents. This is related to non-uniqueness phenomena forweak solution of the same equation. The proof is based on
dynamical systems arguments.

Hao Wu, Fudan University
Analysis of a diffuse interface model for two-phaseincompressible flow in porous medium [canceled]
We study a diffuse interface model for incompressible twophase flows in a porous medium. Existence of global weaksolutions in the three dimensional case is established by using
the monotone operator method. In the two-dimensional case,
we prove the existence and uniqueness of global strong solutions.
Finally, we show that weak solutions of our system will converge
to the weak solution of the Cahn–Hilliard-Darcy system as theviscosity parameter vanishes.

Tue 09:50–11:50

Minisymposium

Minisymposium
Tue 09:50–11:50 Room 1

22

Parallel Sessions Abstracts Tue 09:50–11:50

Minisymposium
Tue 09:50–11:50 Room 3Freeboundary
problems
forhyperbolic/mixed-type PDEs (Part I)

nonlinear

Organizer: G.-Q. Chen

Myoungjean Bae, KAIST
Recent Progress on the Study of Euler-Poisson system
In this talk, I will present recent results on three types(subsonic, supersonic, smooth transonic) of solutions to thesteady Euler-Poisson system
Tue 12:45–14:45

div (ρu) = 0 x

divx (ρu ⊗ u) + ∇x p = ρ∇x φ
divx (ρuB) = ρu · ∇x Φ
∆x Φ = ρ − ρIThis talk is based on several joint works with B. Duan (Dalian
University of Technology), H. Park (Yonsei University), J.-J.
Xiao (Chinese University of Hong Kong) and C. Xie (Shanghai
Jiao Tong University)

Hyangdong Park, Yonsei University
Contact discontinuities for inviscid compressible flows
We prove the existence of a subsonic axisymmetric weaksolution to steady Euler system in a three-dimensional infinitely
long cylinder when prescribing the values of the entropy andangular momentum density at the entrance by piecewise C 2
functions with a discontinuity on a curve on the entrance. Dueto the variable entropy and angular momentum density conditions with a discontinuity at the entrance, the corresponding
solution has a nonzero vorticity, nonzero angular momentum
density, and contains a contact discontinuity. We construct
such a solution via Helmholtz decomposition. (This is a joint
work with Myoungjean Bae.)

Tao Wang, Wuhan University
Free Boundary Problems in Ideal Compressible MHD
I will present the joint works with Professor Yuri Trakhinin on
the local well-posedness of free boundary problems in ideal compressible MHD with or without surface tension. The RayleighTaylor sign condition on the total pressure is required only forthe case of zero surface tension.

Wei Xiang, City University of Hong Kong
Stability of contact discontinuity in nozzles
There can be contact discontinuities in the nozzle for thecompressible Euler flow. In this talk, we will talk about the casesof the subsonic-subsonic, subsonic-supersonic, and supersonicsupersonic contact discontinuity in nozzles and establish thewell-posedness results.

Parallel Sessions Abstracts Tue 12:45–14:45

23

Tue 12:45–14:45
Minisymposium
Tue 12:45–14:45 Room 1

discuss patient specific parameter estimation using reducedorder modeling.

Phase field models (Part II)
Organizers: E. Rocca, V. Styles

We present some recent results on a class of phase-fieldmodels for tumour growth, coupling a nonlocal viscous Cahn–
Hilliard equation for the phase-variable (local concentration oftumoral cells) and a reaction-diffusion equation for the nutrient
concentration (e.g. glucose). The presence of chemotaxis andactive transport terms is also accounted for. We first discuss
weak/strong well-posedness of the system, separation properties for the phase-variable in case of singular potentials, andvanishing-viscosity asymptotics. Secondly, we investgate someselected optimal control problems associated to optimality oftreatment or parameter identification. This study is based on
joint works with Elisabetta Rocca and Andrea Signori.

Björn Stinner, University of Warwick
Automatic phase field regularisation of moving boundary problems
We present a software interface that enables users to specify
moving boundary problems that then are transformed into aphase field model, which subsequently can be solved by binding
to efficient finite element software backends. Many moving
boundary problems amenable to a phase field approximation
have a common structure, namely, equations of gradient flow
type of an interfacial energy are coupled with some balance
laws. We discuss a preliminary classification of such problems
and, with examples, illustrate how the software symbolicallymanipulates the input parameters into the variational formulation of a phase field model. We also address variants ofregularisation and time-discretisation, and the specification of
the spatial discretisation including adaptivity and numericalsolvers.

Marita Thomas, Weierstrass Institute for Applied Analysis
and Stochastics
Convergence analysis for fully discretized damage andphase-field fracture models
This presentation deals with techniques for the spatial andtemporal discretization of models for rate-independent damage
and phase-field fracture featuring a gradient regularization anda non-smooth constraint due to the unidirectionality of thedamage process. Both quasi-static and dynamic evolution of
the displacements is addressed. Suitable notions of solution for
the non-smooth process are introduced and the corresponding
discrete version is studied by combining a time-discrete schemewith finite element discretizations of the domain. Results andchallenges on the convergence of the discrete problems in thesense of evolutionary Gamma-convergence in dependence ofthe choice of the time-discrete scheme, the gradient term andthe mesh properties are discussed.

Harald Garcke, Universität Regensburg
Cahn–Hilliard-Brinkman models for tumour growth
Tumour growth models have been successful in describing
many phenomena relevant for medical applications. We will
introduce phase field systems for tumour growth by coupling
the Cahn–Hilliard equation to a diffusion equation for a nutrient.
In addition, also a coupling to flow equations of Darcy-, Stokesand Brinkman-type are discussed. We will present existence
and uniqueness results, study sharp interface limits and briefly

Tue 12:45–14:45

Luca Scarpa, Politecnico di Milano
On a class of nonlocal phase-field models for tumour
growth24

Parallel Sessions Abstracts Tue 12:45–14:45

Minisymposium
Tue 12:45–14:45 Room 2

UQ in free boundary problems
Organizers: H. Harbrecht, M. D. Multerer

Caroline Geiersbach, Weierstrass Institute
Stochastic Approximation for Optimization in ShapeSpacesTue 17:05–19:05

In this talk, we present a novel approach to solve stochastic
shape optimization problems. Our approach is the extension of
the classical stochastic gradient method, dating back to Robbins
and Monro (1951), to infinite-dimensional shape manifolds. The
basic paradigm of stochastic approximation is the use of partial
function information combined with decreasing step sizes. We
prove convergence of the method on Riemannian manifolds
and make the connection to shape spaces. The method isdemonstrated on an interface identification problem, where
uncertainty arises in the form of a random partial differential
equation. We verify conditions for convergence for the model
problem and demonstrate the method numerically. (Joint workwith Kathrin Welker and Estefania Loayza-Romero.)Alexey Chernov, University of Oldenburg
Numerical solution of rough random obstacle problems
The obstacle problem is a prominent free boundary problem
that consists of finding the profile of an elastic membrane inequilibrium under the constraint that it is located above a given
obstacle function. We are particularly interested characterizing
solutions for a class of rough randomly perturbed obstacles
that may model rough manufactured materials (e.g. asphalt
road surface) or rough biological microstructures. Importantly,
due to randomly changing location of the free boundary, theparameter-to-solution map has only limited global regularitythat makes various polynomial-based approximation methodsof Numerical Uncertainty Quantification notoriously inefficient.
We propose and analyse a family of Multilevel Monte Carloalgorithms that do not suffer from this lack of regularity.

Nick Wulbusch, University of Oldenburg
Shape optimization algorithms for elliptic problems
under uncertainty
We consider a stochastic PDE constrained shape optimization problem. The constraint is represented by a stationary
diffusion problem having a source term with an uncertain location. A typical goal functional represents the misfit between
the computed solution and a prescribed function within thecomputational domain. The aim is to determine the optimal
shape of the domain boudary minimizing the goal functional.
We investigate theoretically and numerically convergence of
gradient-based optimization algorithms and discuss possible
extensions to the time-harmonic acoustic problems in the low
frequency regime.

Helmut Harbrecht, University of Basel
Solving a Bernoulli type free boundary problem withrandom diffusion
The present talk is concerned with the numerical solution ofa free boundary problem for an elliptic state equation with random diffusion. The domain under consideration is represented
by a level set function which is evolved by the objective’s shape
gradient. The state is computed by the finite element method,where the underlying triangulation is constructed by means ofa marching cubes algorithm. The high-dimensional integral,which is induced by the random diffusion, is approximated by
the quasi-Monte Carlo method. By numerical experiments, wevalidate the feasibility of the approach.

Parallel Sessions Abstracts Tue 17:05–19:05

25

Tue 17:05–19:05

Numerical methods for geometric PDEs (Part I)
Organizers: R. Nochetto, R. Nürnberg

Andrea Bonito, Texas A&M University
Numerical Approximations of Plates Undergoing
Large Deformations and Folding
Thermostats, microgrippers, sensors, telescopes, selfdeployable structures, growth in soft tissues, growth in leaves
or fungus, nano actuators, flapping and flytrap mechanisms,
and origami are diverse examples among many others wherea plate-like device undergo large deformations. With theseapplications in mind, we consider thin sheets endowed withdifferent elastic energies modeling either lattice mismatches
between two layers of polymers, internal stresses, or defects
in the materials. Their common feature is that they resultin forth order problems for the plate deformation. However,the possibility of large deformations rules out standard linear
models. Instead, the first fundamental forms of the platedeformations are constrained to the identity, if the platecannot sustain shear nor stretch, or more generally to agiven prestrain metric. The numerical algorithms for theapproximation of the plate deformations are based on local
discontinuous Galerkin methods, where high order derivatives
in the continuous models are replaced by weakly converging
discrete reconstructions. We briefly describe the models,algorithms along with their analysis, and explore numericallytheir capabilities.

Wenbo Li, University of Tennessee, Knoxville
Finite element discretizations of nonlocal minimal
graphsWe study the discretizations of nonlocal minimal graphs oforder s ∈ (0, 1/2), minimizing the so-called fractional perimeters. Such a Plateau problem can be reinterpreted as a Dirichletproblem for a nonlocal, nonlinear, degenerate operator of orders + 1/2. We propose a numerical method based on piecewise linear Lagrange finite elements on shape-regular meshes,and prove existence, uniqueness and convergence of discrete
solutions. In addition, We derive error estimates for a novel
geometric quantity related to the concept of fractional normal.
We also present numerical experiments that illustrate the performance of our scheme and behaviors of nonlocal minimal
graphs including the stickiness phenomenon. This is a joint
work with Juan Pablo Borthagaray and Ricardo H. Nochetto.

Shawn Walker, Louisiana State University
A Mixed FEM for the Plate Equation on Surfaces:
the Surface HHJ Method
We present a mixed finite element method for solving afourth order elliptic PDE, the Kirchhoff plate equation, on
a surface embedded in R3 , with or without boundary. The
method discretizes the surface Hessian directly, is built on
the classic Hellan–Herrmann–Johnson (HHJ) method (for flat
domains), and convergence is established for a C k+1 surface,with C 0 , degree k (Lagrangian) approximation of the surface,
for any k ≥ 1. Mixed boundary conditions are allowed, including
clamped, simply-supported, and free conditions. Numericalexamples are presented that demonstrate the method, the useof “point” boundary conditions, and how to solve the surface
biharmonic equation, which has many applications, such as
surface (thin film) flows and surface diffusion.

Sören Bartels, University of Freiburg
Local Mesh Refinement in the Numerical Approximation of TV Regularized Variational Problems
Recent quasi-optimal error estimates by Chambolle and Pockfor the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz
continuous dual solution. We discuss the validity of this condition and devise numerical methods using locally refined meshes
that lead to improved convergence rates despite the occurrenceof discontinuities. It turns out that linear convergence is possible on suitably constructed meshes. This is joint work withFriedrich Wassmer (University of Freiburg).

Tue 17:05–19:05

Minisymposium
Tue 17:05–19:05 Room 1

26

Parallel Sessions Abstracts Tue 17:05–19:05

Contributed Session
Tue 17:05–19:05 Room 2Contributed session (Part I)
Diogo Caetano, University of Warwick
The Cahn–Hilliard equation on an evolving surface

Tue 17:05–19:05

We describe a setting for posing evolution PDEs on evolving hypersurfaces which is suitable for formulating the Cahn–
Hilliard equation on a moving surface. We consider wellposedness for smooth, logarithmic, and double obstacle nonlinearities and with a constant mobility term. It turns out thatfor the singular potentials some conditions relating the initial
data and the evolution of the surfaces are necessary for (global
in time) existence of solutions, and we identify these different
regimes. We then consider a related model that does not preserve the integral of solutions, and establish existence results.
Time permitting, we will also discuss some open questions andrelated problems. This is joint work with Charlie Elliott (U. of
Warwick).

Lars von Wolff, University of Stuttgart
A Ternary Cahn–Hilliard Navier–Stokes Model for
Two Phase Flow with Precipitation and Dissolution
Multiphase flow and reactive transport are important in many
applications, for example in porous media. We consider theincompressible flow of two immiscible fluids in the presence ofa solid phase changing due to precipitation and dissolution ofions. We propose a novel phase-field model that extends thewidespread two-phase models to the ternary case by including
a solid phase. Here the fluid-solid interaction poses new difficulties. The model obeys the second law of thermodynamics fora free energy including the ion concentration. We analyze the
sharp interface limit, in particular for the three-phase contact
point. Notably, the new phase-field model realizes Navier-slip
conditions for solid-fluid interfaces. We conclude with a comparison of numerical simulations with experimental data.

Alice Marveggio, Institute of Science and Technology Austria (IST)
On a non-isothermal Cahn–Hilliard model based ona microforce balance
We consider a non-isothermal Cahn–Hilliard model basedon a microforce balance. The model was derived by A. Miranville and G. Schimperna starting from the two fundamental
laws of Thermodynamics, following M. Gurtin’s two-scale approach. The main working assumptions are on the choice of
the Ginzburg-Landau free energy, and on the behaviour of theheat flux as the absolute temperature tends to zero and toinfinity. By deriving suitable a priori estimates and by showing
weak sequential stability of families of approximating solutions,
we prove global-in-time existence for the initial-boundary value
problem associated to the entropy formulation and, in a subcase, also to the weak formulation of the model. (Joint workwith G. Schimperna)

Makoto Okumura, Hokkaido University
The solvability of a discrete variational derivative
scheme for the equation and boundary condition of
the Cahn–Hilliard typeIn this talk, we propose a structure-preserving scheme for theCahn–Hilliard equation with dynamic boundary conditions introduced by Goldstein et al. (2011). In this model, the total massconservation and the total energy dissipation hold. We design
a structure-preserving scheme for the target equation so thatthe scheme retains the properties using the discrete variational
derivative method proposed by Furihata-Matsuo (2010). Then,
how to discretize the energy which characterizes the equation,

it is important and essential. Indeed, modifying the conventional manner and using an appropriate summation-by-parts
formula, we improve the structure-preserving scheme for thetarget problem. Also, we prove the solvability of the proposed
scheme and show the results of numerical experiments.

Parallel Sessions Abstracts Tue 17:05–19:05

Contributed Session
Tue 17:05–19:05 Room 3

Contributed session (Part II)
Dominik Edelmann, Eberhard Karls Universität Tübingen27

produces technical difficulties for the PDE estimates. I will
discuss the stability results we obtained concerning this model.
Through stability analysis, the results indicate that tumor withlarge aggressiveness parameter would trigger instability, which
is biologically reasonable.

We present convergence results for the evolving finite element
semi-discretization of a parabolic partial differential equation
on an evolving bulk domain. The boundary of the domain
evolves with a given velocity, which is then extended to thebulk by solving a Poisson equation. The numerical solution
to the parabolic equation depends on the numerical evolutionof the bulk, which yields the time-dependent mesh for thefinite element method. We provide error estimates that are of
optimal order in H 1 -norm and present a sketch of the proof,
addressing the main difficulties. Various numerical experiments
are presented. In conclusion, we give an outlook on future
work.

Kota Kumazaki, Nagasaki University
Large time growth of swelling moving interfaces ona halfline
In cold regions, buildings that are exposed to extremely low
temperatures undergo freezing and build microscopic ice lenses
that lead to the mechanical damage of the material. In thistalk, we consider a free boundary problem as a mathematicalmodel describing swelling of water to understand the ice lenses
formation growing inside of porous materials. Our problem
is posed on a halfline with a moving boundary at one of theends, and the moving boundary conditions encode the swellingmechanism, while a diffusion equation provides water content
for the swelling to take place. In this talk, we discuss the global
existence and uniqueness of a solution to our problem and givethe result of the large time behavior of a solution as time goesto infinity.

Martin Weiser, Zuse Institute Berlin
Multilevel Augmented-Lagrangian Methods for Overconstrained Contact Discretizations
We consider overconstrained formulations for stationary
multi-body contact and adapted multilevel solvers of augmented Lagrange type for the resulting QPs. We discretize
non-penetration by a simple symmetric, pointwise sampling
without a priori choice of master and slave sides. The drawbackis, that the multiplier discretization is not of the special structure provided by dual mortar spaces. This prevents the use of
efficient nonlinear Gauss-Seidel smoothers as done in monotone
multigrid methods. We use an augmented Lagrangian solver
combined with a primal multigrid hierarchy and overlapping
nonlinear block Gauss-Seidel smoothers, exploiting high arithmetic density of local penalized problems. Effective coarse gridcorrections in sliding contact are achieved by level-dependent
penalties.

Xinyue Zhao, University of Notre Dame
A Free Boundary Tumor Growth Model with a Time
Delay
In this talk, I will present a non-radially symmetric tumor
growth model with a time delay in cell proliferation. The timedelay represents the time taken for cells to undergo replication(approximately 24h). The model is a coupled system of an elliptic equation, a parabolic equation and an ordinary differential
equation. It incorporates the cell location under the presence oftime delay, with the tumor boundary as a free boundary. The inclusion of a small time delay makes the system non-local, which

Tue 17:05–19:05

Finite element analysis for a diffusion equation on aharmonically evolving domain

28

Parallel Sessions Abstracts Tue 17:05–19:05

Contributed Session
Tue 17:05–19:05 Room 4

Contributed session (Part III)
Nino Khatiashvili, Iv. Javakhishvili Tbilisi State University
On the Free Boundary Problem for 2D flows
The 2D viscous flow with large viscosity and low Reynolds
number (Re«1) is considered in the half-plane. Solutions of
the Stokes system are obtained, when the pressure is harmonic
function. The profiles of free boundaries for the different pressures are constructed. For 2D perfect fluid the free boundary
problem is reduced to the singular integral equation with theWeierstraß kernel for unknown free boundary [1]. The equation
is solved numerically. The profiles of waves with peaks areconstructed.
References:: [1] N. Khatiashvili , On the singular integral equation with the Weierstraß kernel. J. Complex Variables andElliptic Equations, Taylor & Francis, 2008, vol. 53, N 10.

Vladislav Pukhnachev, Lavrentyev Institute of Hydrodynamics
Viscous flows with flat free boundaries
Wed 09:50–11:50

We consider a class of exact solutions for the Navier–Stokes
equations in a plane or axially symmetric case, which describes
the motion in a strip or layer with one or both flat boundaries
being free, while the second boundary can be a solid wall
(problems A and B, respectively). In problem B, sufficientconditions for global existence of the solution or its blow up ina finite time are obtained. There are three regimes of motion
in problem A: stabilization to the quiescent state, blow up in a
finite time, and intermediate regime in which the viscous layeror strip expands infinitely in an infinite time. This talk is basedon joint work with Elena Zhuravleva.

Athanasios Stylianou, Universität Kassel
Modelling pattern formation on the surface of aferrofluid
The talk deals with patterns appearing on the free surface
of a ferromagnetic fluid placed in a vertical magnetic field,
undergoing a so-called Rosensweig instability. We present an
existence theory for periodic and localized patterns, for a corresponding free interface problem, and tackle with the problem
of regularity.

Kyung Ha, UCLA math department
Uniformly distributing microdroplets in microparticles
The creation of fixed-microsized droplets is important forassays and lab-on-chip applications. Recently a new method
has been developed using microsized particles that capture
uniform-sized droplets. For our purposes, the fluid surface will
be in the shape that minimizes the surface tension energy.
We use the well-known results to solve this minimal surface
problem with volume constraints. By plotting the energy fora given volume we can plot the volume-energy graph for agiven particle. Once we obtain the volume-energy graph of aparticle, we develop a mathematical theory based on energy
minimization that explains the uniform distributions of droplets.
This helps us understand the reproducibility of the technology
and help determine the efficient design of the particles.

Parallel Sessions Abstracts Wed 09:50–11:50

29

Wed 09:50–11:50
Minisymposium

Minisymposium
Wed 09:50–11:50 Room 1

Wed 09:50–11:50 Room 2

Surface PDEs (Part I)

Nonlocal free boundary problems (Part I)

Organizers: C. Venkataraman, T. Ranner

Organizers: E. Valdinoci, J.-F. Rodrigues

Philip Brandner, RWTH Aachen University
Stream Function Formulation of Surface Stokes Equations

Alexander Nazarov, St. Petersburg Dept of Steklov Institute and St. Petersburg State University
Variational Inequalities for the Fractional Laplacians

We consider surface Stokes equations on a C 2 simply connected oriented stationary hypersurface Γ ⊂ R3 without boundary and derive a stream function formulation based on a surface
Helmholtz decomposition of these equations. This formulation
results in a fourth order scalar-valued problem. For numericalsimulation purposes the fourth order problem is split in two coupled second order problems, to which a TraceFEM discretization
is applied. Velocity and pressure are reconstructed from theunique stream function solution. An error analysis is available.
Results of numerical experiments are presented which illustratecertain properties of this approach. We draw comparisons between the stream function method and a Taylor-Hood-based
TraceFEM discretization.

We study the obstacle problems for the Dirichlet and Navier
fractional Laplacians of order s ∈ (0, 1) in a bounded Lipschitz
domain Ω ⊂ Rn , under mild assumptions on the data. We
obtain some regularity results and compare the solutions for
two types of Laplacians. This talk is mainly based on the papers
R. Musina, A.I. Nazarov, K. Sreenadh, Potential Analysis, V.
46 (2017), N3, and R. Musina, A.I. Nazarov, Comp. Math.
and Math. Phys., V. 57 (2017), N3. The author was partially
supported by RFBR grant 20-01-00630a.

The closest point method is an embedding method for solving
PDEs on surfaces. Using a closest point representation of
the surface, a constant-along-normal extension is employed
to formulate the PDE in the embedded space, which can besolved numerically using standard finite difference schemes.
We present a closest point method that uses finite difference
schemes derived from radial basis functions (RBF-FD). Using
RBF-FD, a smaller computational domain surrounding thesurface is required, resulting in a decrease in the number ofsampling points on the surface. The method uses RBF centerson regular grid nodes, avoiding the ill-conditioning that may
arise from point clustering on the surface. Numerical tests
include a number of applications on static and moving surfaces.

Marino Arroyo, Universitat Politecnica de CatalunyaBarcelonaTech
Free boundary problems in cell mechanobiology
Interfacial mechanical and chemical phenomena control the
shape, motion, mechanical properties, and many functions inanimal cells. I will present mathematical models and simulationsof membrane shaping by proteins, cytoskeletal dynamics, andadhesion dynamics pertinent to cell mechanobiology.

We study the probability measures ρ ∈ M2 minimizing thefunctional

ZZ
J[ρ] =

log1dρ(x)dρ(y) + d2 (ρ, ρ0 ),|x − y|where ρ0 is a given probability measure and d(ρ, ρ0 ) is the 2Wasserstein distance of ρ and ρ0 . J[ρ] appears in aggregation
models when the movement of particles is advanced by thepotential − log |x| ∗ ρ. We prove the existence of minimizers
ρ and show that the potential U ρ = − log |x| ∗ ρ solves adegenerate obstacle problem, the obstacle being the transportpotential. Among other things, we study the regularity ofminimizers and the structure of singular set of free boundary.

Xavier Fernández-Real, EPFL
Stable cones in the thin one-phase problem
The fractional or thin one-phase problem is the study ofminimizers of the functionalJs (u) = [u]2H s (B1 ) + |{u > 0} ∩ B1 |.
The aim of this talk is to study homogeneous stable solutions to
the fractional one-phase free boundary problem. The problem
of classifying stable (or minimal) homogeneous solutions indimensions n ≥ 3 is completely open. In this context, axiallysymmetric solutions are expected to play the same role as
Simons’ cone in the classical theory of minimal surfaces, buteven in this simpler case the problem is open. The goal ofthis talk is twofold and is based on a recent work with X. RosOton. On the one hand, we present our first main contribution:
the stability condition for the thin one-phase problem. Quite
surprisingly, this requires the use of “large solutions” for thefractional Laplacian, which blow up on the free boundary. On
the other hand, using our new stability condition, we showthat any axially symmetric homogeneous stable solution indimensions n ≤ 5 is one-dimensional, independently of theparameter s ∈ (0, 1).

Juan Luis Vázquez, Universidad Autónoma de Madrid
Nonlocal free boundary problems of porous medium
type
The property of finite propagation and existence of free or
free boundaries is well known in the theory of nonlinear elliptic
and parabolic equations of nonlinear degenerate diffusive type.
When the Laplacian type diffusivity is replaced by nonlocal
operators, like fractional operators, such a property is or is

Wed 09:50–11:50

Argyrios Petras, Johann Radon Institute for Computational and Applied Mathematics (RICAM)An RBF-FD closest point method for solving PDEs
on surfaces and applications to PDEs on moving
surfaces

Aram Karakhanyan, University of Edinburgh
A nonlocal free boundary problem with Wasserstein
distance

30

Parallel Sessions Abstracts Wed 09:50–11:50

not conserved depending on the balance between de degenerate nonlinearities and the nonlocal character of the fractional
diffusion.

Minisymposium
Wed 09:50–11:50 Room 3

Stochastic free boundary problems (Part I)
Organizers: A. Djurdjevac, B. Gess, G. Grün

Lubomir Banas, Bielefeld University
Convergent numerical approximation of the stochastic porous media equation in higher dimensions.
We propose a fully discrete numerical scheme for the approximation of the stochastic porous media equation (SPME)
in its very weak formulation. Using the monotonicity properties of the very weak formulation we show that the proposed
numerical scheme converges to the strong solution of SPME.
We construct a non-standard finite element based spatial approximation of the problem which yields an efficient numericalalgorithm in the spatial dimension d = 2, 3. We present numerical experiments to illustrate the behavior of the proposed
numerical algorithm. The talk is based on a joint work with
Benjamin Gess and Christian Vieth.

Nicolas Dirr, Cardiff University
Probability and Analysis in Multi-Scale Systems
Wed 09:50–11:50

We give an overview over recent results, both rigorous andnumerical, for multiscale problems where there is nonlinear
diffusion on the macro-scale and a high-dimensional stochastic
system on the micro-scale.

Hubertus Grillmeier,Friedrich-Alexander-Universität
Erlangen-Nürnberg
Stochastic porous-medium equations: a sufficientcondition for a.s. instantaneous propagation of freeboundaries
For stochastic porous-medium equations with multiplicative
linear source-term noise, Fischer and Grün recently formulated
sufficient conditions on the growth of initial data close to thefree boundary which guarantee the occurrence of a waitingtime phenomenon, i.e., a delayed onset of propagation of thefree boundary. In this talk, we study the reverse problem. We
rigorously identify new growth conditions sufficient for instantaneous spreading of solutions almost surely. For this, we derive
an upper bound for the average time at which solutions begin to spread. Technically, we combine Ito-formulas including
random stopping times with weighted integral estimates. It
is worth mentioning that these results are not confined to
Lipschitz-regular noise terms.

Sebastian Hensel, Institute of Science and Technology Austria (IST)
Finite time extinction for the 1D stochastic porous
medium equation with transport noise
We establish finite time extinction with probability one for
the Cauchy-Dirichlet problem of the 1D stochastic porous
medium equation with Stratonovich transport noise and compactly supported smooth initial datum. This is expected since1
Brownian motion has average spread rate O(t 2 ) whereas the
support of solutions to the deterministic PME grows only with
1
rate O(t m+1 ). I will discuss the three main ingredients fora rigorous implementation of this heuristic: i) a contraction
principle up to time-dependent shift for Wong-Zakai type approximations, ii) the transformation to a deterministic PMEwith two copies of a Brownian path as the lateral boundary,and iii) the construction of a maximal subsolution for the latterproblem in terms of the pressure variable.

Parallel Sessions Abstracts Wed 09:50–11:50

31

Minisymposium
Wed 09:50–11:50 Room 4

Geometric problems (Part II)
Organizers: M. Novaga, Y. Giga

Paola Pozzi, University of Duisburg-Essen
On the elastic flow networks
We call a network the union of sufficiently smooth curves
that meet at junctions. The simplest configuration is a threenetwork: this is the union of three curves that meet at one
or two junctions. In the first case we speak of a triod, in thesecond of a theta-network. Networks and flow of networks
arise naturally in the study of multiphase systems and when
considering the dynamic of their interfaces. In this talk I will
present recent results for the elastic flow of three-networks.

Nonlocal energies are continuum models for large systems ofparticles with long-range interactions. Under the assumptionthat the interaction potential is radially symmetric, several
authors have investigated qualitative properties of energy minimisers. But what can be said in the case of anisotropic potentials? Starting from the example of dislocations in materials
science, I will discuss some results and partial answers on how
anisotropy affects the shape and dimension of the support ofminimisers. This is based on work in collaboration with Jose
Antonio Carrillo, Joan Mateu, Maria Giovanna Mora, Luca
Rondi and Joan Verdera.

Ulisse Stefanelli, University of Vienna
Rate-independent evolution of sets
I will present a model for the rate-independent evolutionof sets with finite perimeter. The evolution is driven by agiven time-dependent forcing set, acting as a one-sided constraint. Solutions result from the quasistatic competition between perimeter minimization and minimization of volume
changes. This idealized setting arises in connection with delamination models in the so-called brittle limit and provides asort of rate-independent mean-curvature flow. I will commenton this point and present existence and approximation results.
In the two-dimensional case, the geometry and regularity ofsolutions will be assessed and some numerical results will bepresented. This is a joint work with Riccarda Rossi (Brescia)
and Marita Thomas (Berlin).

Mathias Wilke, Martin-Luther University Halle-Wittenberg
On the Navier–Stokes equations on surfaces
We consider a model for the motion of an incompressible
viscous fluid that completely covers a smooth, compact hypersurface Σ in Rd+1 and flows along Σ. Several questions
related to well-posedness and the qualitative behavior are addressed. This is a joint work with Jan Prüss and Gieri Simonett(Vanderbilt University, Nashville, TN, USA)Wed 12:45–14:45

Lucia Scardia, Heriot-Watt University
Equilibrium measures for nonlocal energies: The effect of anisotropy32

Parallel Sessions Abstracts Wed 12:45–14:45

Wed 12:45–14:45
Minisymposium

Minisymposium
Wed 12:45–14:45 Room 1

Wed 12:45–14:45 Room 2

Regularity of free boundaries (Part I)

Numerical methods(Part II)

Organizers: H. Shahgholian, M. Smit Vega Garcia

Jinwan Park, Seoul National University
The Regularity Theory for the Double Obstacle Problems
In this talk, I will introduce the regularity of the free boundary
for the double obstacle problems. Precisely, I will discuss theinterior C 1 regularity of the free boundary for the elliptic andparabolic double obstacle for linear and fully nonlinear operator.
Furthermore, I will introduce the C 1 regularity of the freeboundary near fixed boundary for Laplacian problem. The
contents are based on the paper and pre-prints, joint works
with Professor Henrik Shahgholian and Ki-Ahm Lee.

Sunghan Kim, KTH Royal Institute of Technology
On an elliptic free boundary problem arising fromjump of conductivity
When a composite material changes its conductivity along
the phase transition, it can be mathematically modelled by anelliptic PDE whose coefficient changes discontinuously alongcertain level surface of the associated solution. Such a level surface becomes the free boundary. In this talk, we shall consider
one such problem given bydiv(A(x, u)∇u) = 0,
Wed 12:45–14:45

where conductivity matrix A(x, u) has a jump across the zerolevel set, {u = 0}, of a given solution u, but is smooth elsewhere.
We shall discuss the regularity of the free boundary near a nondegenerate point, the structure of the singular set, and the
behaviour of the free boundary near a fixed boundary. This ispartially based on a joint work with Ki-Ahm Lee and Henrik
Shahgholian.

Nicola Soave, Politecnico di Milano
Free boundary problems in the spatial segregation ofcompeting systems
In this talk we present some results concerning the spatial
segregation in systems with strong competition. In particular, we focus on two different (but strongly related) issues:
long-range segregation models and systems characterized byasymmetric diffusion. The content of the talk is part of ongoingproject with H. Tavares, S. Terracini and A. Zilio.

Simon Eberle, University of Duisburg-Essen
On global solutions of the obstacle problem
In this talk we investigate global solutions of the classicalobstacle problem. I give a partial result towards a conjectureby H. Shahgholian (’92) saying that the coincidence sets ofglobal solutions of the obstacle problem are in the closure ofellipsoids, i.e. ellipsoids, paraboloids, cylinders with one of thetwo as basis, or half-spaces. I give a short proof of the known
result that bounded coincidence sets of global solutions of the
obstacle problem that have non-empty interior are ellipsoids.
My main and new result is that in dimensions greater or equal
to 6 coincidence sets of global solutions, that are not constantin any direction are paraboloids if they have non-empty interior.

for surface-bulk problems

Organizers: A. Reusken, E. Bänsch

Stefan Metzger, FAU Erlangen-Nürnberg
On the numerical treatment of Cahn–Hilliard equations with dynamic boundary conditions
This talk addresses the numerical treatment of a family ofmodels coupling Cahn–Hilliard type equations in the domain
and on the boundary. All of these models describe an evolution
minimizing the sum of Ginzburg-Landau type free energies inthe bulk and on the surface, but differ in the equilibration rate of
the corresponding chemical potentials. The system describing
the limit case of instantaneous equilibration was proposed andanalysed by Goldstein, Miranville, and Schimperna (Physica
D, 2011), while the case of no equilibration was investigatedby Liu and Wu (Arch. Ration. Mech. Anal, 2019). We will
present a stable, convergent, fully discrete finite element schemethat is able to deal with the complete class of models. The
results presented in this talk are based on a joint work withPatrik Knopf (Universität Regensburg), Kei Fong Lam (HongKong Baptist University), and Chun Liu (Illinois Institute ofTechnology).

Robert Nürnberg, University of Trento
Fluidic two-phase biomembranes: Numerical analysis
and computations
A parametric finite element approximation of a fluidic membrane, whose evolution is governed by a surface Navier–Stokes
equation coupled to bulk Navier–Stokes equations, is presented.
The elastic properties of the membrane are modelled with thehelp of curvature energies of Willmore and Helfrich type. We
allow for two different phases to be present on the membrane,with their own elastic properties, giving rise to an additionalline energy. This is modelled with the help of a phase field thatevolves according to a surface Cahn–Hilliard equation. In thistalk we investigate some desirable properties of the scheme, including stability and good mesh properties, and present several
numerical simulations.

Thomas Ranner, University of Leeds
Numerical analysis of a coupled bulk-surface problem
in an evolving domain
Based on an abstract theory for continuous in time finite
element discretisations of partial differential equations posedin evolving domains, I will present numerical analysis of asimple coupled bulk-surface problem. The problem couples
a linear parabolic equation in the evolving bulk domain to alinear parabolic equation posed on the boundary surface of thedomain. Evolving bulk and surface isoparametric finite element
spaces defined on evolving triangulations will be developed.
Optimal a priori bounds are shown under usual assumptions on
the geometry and solution of the partial differential equation.
We conclude with a numerical example.

Alfred Schmidt, University of Bremen
Phase transitions with free surface flow: a 3D FEM
with a Young-Laplace formulation
Problems with melting and solidification including free surface flow of the melt arise in models for applications like welding
or laser melted material accumulation. They pose special challenges to the numerical discretization and solution. Both sharp
interface and implicit phase boundary formulations with freesurface flow have pros and cons in some situations, a combination of both may lead to stable method, but is applicable only

Parallel Sessions Abstracts Wed 12:45–14:45

Minisymposium
Wed 12:45–14:45 Room 3

Optimization and control of FBPs (Part II)
Organizers: M. Hintermüller, M. Hinze

René Pinnau, TU Kaiserslautern
Optimal Control of FBVPs in Filter Production [canceled]
In this talk we present different FBVPs in filter production
and corresponding optimal control problems. These include
the production of the fibre material as well as the control of
the filtration process. The problems are analysed and we use
the adjoint variables to derive the derivative information which
is needed for the respective numerical solution. Further, we
discuss possible relaxations and approximations.

Dmytro Strelnikov, TU Ilmenau
Optimal control for crack-free pulsed laser beam welding of aluminium alloys
The laser welding process consists of the melting and thesolidification stages. Our goal is to avoid the material cracking
due to its fast solidification by choosing the laser power mode.
The process may be modeled as a BVP with the heat equation
at its core. The equation coefficients are temperature dependent in order to properly take different modes of heat transfer
and the phase transition into account. The interface between
the solid and the liquid regions is not known at the outsetof the problem and is time dependent. The mathematical formulation of the problem is set up and the numerical modelis implemented using the finite-element software FEniCS. We
solve an optimal control problem for the laser power modeby minimizing the cost functional based on the solidification
velocity.

Patrik Knopf, Universität Regensburg
Phase-field methods for spectral shape and topology
optimization
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting
the shape of the domain on which the eigenvalue problem isconsidered. Here, a phase-field function is used to represent theshapes over which we minimize. The idea behind this method
is to modify the Laplace operator by introducing phase-fielddependent coefficients in order to extend the eigenvalue problem on a fixed design domain containing all admissible shapes.
The resulting shape and topology optimization problem canthen be formulated as an optimal control problem with PDE
constraints in which the phase-field function acts as the control.
For this optimal control problem, we present first-order necessary optimality conditions and several numerical simulations.

Björn Baran, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg
Feedback Control of the Stefan Problem
We discuss the feedback stabilization of a two-dimensional
two-phase Stefan problem coupled with (Navier-)Stokes equations. The Stefan problem can model solidification and meltingof pure materials and gets its name from the purely algebraic
Stefan condition which describes the coupling between thetemperature of the material and its melting process. After linearization and discretization, the stabilization problem results
in a non-autonomous differential Riccati equation (DRE) withdifferential-algebraic structure. We present novel techniques totreat the specific structure of this coupled problem in a DRE
solver and illustrate its performance using numerical examples.

Wed 12:45–14:45

in special cases. Especially in 3D, this is often not the case.
We propose a model with a Young-Laplace formulation forthe capillary melt surface shape, and present a corresponding
3D finite element method and numerical results. This is joint
work with Henrik Ücdemir, Eberhard Bänsch, Mischa Jahn,
and Andreas Luttmann

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Minisymposium
Wed 12:45–14:45 Room 4Interfaces in fluids (Part III)
Organizers: H. Abels, H. Garcke, M. Wilke

Andrea Giorgini, Indiana University
Well-posedness of the Abels-Garcke-Grün model for
two-phase flows
The Abels-Garcke-Grün (AGG) system is a diffuse interface
model describing multi-phase fluid flows. This was proposed
as a generalization of the well-known Model H in the case of
unmatched homogeneous densities of the fluids. The model
consists of a Navier–Stokes-Cahn–Hilliard system characterized
by a concentration-dependent density and an additional flux
term due to interface diffusion. Using the method of matchedasymptotic expansions, the sharp interface limit of the AGG
model corresponds to the two-phase Navier–Stokes equations.
In the literature, the analysis of the AGG system has been
mainly focused on the existence of weak solutions. In this talk,I will present some recent results on the existence, uniquenessand stability of strong solutions for the AGG model.

Ian Tice, Carnegie Mellon University
Traveling wave solutions to the free boundary Navier–Stokes equations

Wed 16:15–18:15

Consider a layer of viscous incompressible fluid bounded below by a flat rigid boundary and above by a moving boundary.
The fluid is subject to gravity, surface tension, and an external
stress that is stationary when viewed in coordinate systemmoving at a constant velocity parallel to the lower boundary.
The latter can model, for instance, a tube blowing air on thefluid while translating across the surface. In this talk we will
detail the construction of traveling wave solutions to this problem, which are themselves stationary in the same translating
coordinate system. While such traveling wave solutions to theEuler equations are well-known, to the best of our knowledge
this is the first construction of such solutions with viscosity.
This is joint work with Giovanni Leoni.

Maurizio Grasselli, Politecnico di Milano
Nonlocal Cahn–Hilliard-Hele-Shaw systems
I intend to present some recent results on nonlocal Cahn–
Hilliard-Hele-Shaw systems focusing on a model characterized
by noncostant mobility, singular potential, and nonconstantkinematic viscosity. Well-posedness and regularity issues will
be discussed. These results have been obtained jointly with
C. Cavaterra and S. Frigeri (Università degli Studi di Milano,
Italy).

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35

Wed 16:15–18:15
Minisymposium

Minisymposium
Wed 16:15–18:15 Room 1

Wed 16:15–18:15 Room 2

Numerical methods for geometric PDEs (Part II)

Free boundary models in active matter

Organizers: R. Nochetto, R. Nürnberg

Organizer: L. Berlyand

Antonin Chambolle, CNRS and CEREMADE, Université
Paris-Dauphine, PSL, France
Learning better discretizations of the total variation

Leonid Berlyand, Penn State University
Asymptotic Stability in an FBP model of ContractionDriven Cell Motion

In this talk I will describe two approaches to improve consistent discretizations of the total variation, (1) by designing aperiodic pattern and homogenization (2) by learning a templatefor enforcing constraints in the dual formulation. This is joint
works with T. Pock (Graz), L. Kreutz (Münster)

We introduce a free boundary model of the onset of motionof a living cell (e.g. a keratocyte) driven by myosin contraction
with focus on a transition from unstable radial stationary states
to stable asymmetric moving states. This model generalizes
a previous 1D model (Truskinovsky et al.) by combining a
Keller-Segel model, a Hele-Shaw boundary condition and theYoung-Laplace law with a nonlocal regularizing term which precludes blow up or collapse by ensuring that membrane-cortex
interaction is sufficiently strong. We show that this model has
a family of asymmetric traveling wave solutions bifurcatingfrom a family of stationary states. Our goal is to establish
observable steady cell motion with constant velocity. Mathematically, this amounts to proving stability of the travelingwave solutions, which requires generalization of the standard
notion of stability. Our main result is establishing nonlinear
asymptotic stability of traveling solutions. To this end, we derive an explicit asymptotic formula for the stability-determining
eigenvalue from asymptotic expansions in small speed. This
formula greatly simplifies the numerical computation of thesign of this eigenvalue and reveals the physics underlying onsetof the cell motion and stability of moving states. This is joint
work with V. Rybalko and C. A. Safsten.

We consider the motion of parametric curves by anisotropic
curve shortening flow. We propose a strictly parabolic system
of PDEs for the position vector whose solution satisfies thecorresponding evolution law. This system is discretized by linear
finite elements and optimal H 1 error bounds are proved in thesemidiscrete case. We present numerical experiments whichshow that the scheme has good properties with respect to the
distribution of mesh points. This is joint work with Robert
Nuernberg.

Hanne Hardering, TU Dresden
Tangential errors of tensor surface finite elements
We discretize a tangential tensor field equation using asurface-finite element approach with a penalization term to ensure almost tangentiality. It is natural to measure the quality ofsuch a discretization intrinsically, i.e. to examine the tangential
convergence behavior in contrast to the normal behavior. We
show optimal order convergence with respect to the tangential
quantities in particular for an isogeometric penalization termthat is based only on the geometric information of the discretesurface. This is joint work with S. Praetorius.

Martin Rumpf, Universität Bonn
Finite Element Approximation of Large Scale Isometric Deformations of Parametrized Surfaces
In this talk the numerical approximation of isometric deformations of thin elastic shells is discussed. To this end, for a thinshell represented by a parametrized surface it is shown how totransform the stored elastic energy for an isometric deformationsuch that - similar to the model for plate deformations - thehighest order term is quadratic. For this reformulation existenceof optimal isometric deformations is shown. A finite element
approximation is obtained using the Discrete Kirchhoff Triangle(DKT) approach and the convergence of discrete minimizers to
a continuous minimizer is demonstrated. It that respect, thispaper generalizes the results by Sören Bartels for the approximation of bending isometries of plates. A Newton scheme isapplied to experimentally verified the convergence propertiesand discuss characteristics of isometric deformations. The talkis based on joint work with Stefan Simon and Christoph Smochfrom Bonn.

Ricard Alert, Princeton University
Stability of chemotactic fronts
In contexts ranging from embryonic development to bacterial
ecology, cell populations migrate chemotactically along selfgenerated chemical gradients, often forming a propagating
front. The motion of such chemotactic fronts constitutes a freeboundary problem where the interface is driven by a coupling
between the cell density field and the gradient of the chemical
concentration field. I will analytically show that the linear
stability of chemotactic fronts to morphological perturbations
is determined by limitations in the ability of individual cells
to sense and respond to the chemical gradient. Specifically, I
will argue that cells at a bulging part of the front are exposed
to a smaller gradient, which slows them down and promotes
stability, but they respond more strongly to the gradient, which
speeds them up and promotes instability. We predict that thiscompetition leads to chemotactic fingering when sensing islimited at low chemical concentrations, and to stable flat fronts
when it is instead limited at high concentrations. Guided by thisfinding and by experimental data on bacterial chemotaxis, I will
suggest that the cells’ sensory machinery might have evolved
to ensure stable front propagation. Finally, as sensing of any
stimuli is necessarily limited, the principle of sensing-induced
stability may operate in other types of directed migration suchas durotaxis, electrotaxis, and phototaxis. This is joint workwith Sujit S. Datta at Princeton University.

Jaume Casademunt, University of Barcelona
Symmetry breaking and motility of cells and tissues
Understanding the physical mechanisms that govern cell
motility and collective cell migration is of great importance toa variety of challenging biological problems, from embryogenesis to tissue repair and cancer invasion. To this aim, bothindividual cells and cell colonies are often modeled as quasi-twodimensional droplets of active fluids that define free-boundary
problems. Here we provide a brief overview of several such

Wed 16:15–18:15

Klaus Deckelnick, Otto-von-Guericke-Universität Magdeburg
A novel finite element scheme for anisotropic curve
shortening flow

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models, with particular focus on the interplay between themechanisms of symmetry breaking and directed motion. We
discuss prototype models for individual cells where motility
originates on a spontaneously broken symmetry, either froma purely morphological instability of the boundary, or involving an inhomogeneous distribution of a chemical species that
controls the activity. We then discuss a recently introduced
free-boundary problem based on a hydrodynamic model for cohesive cell tissues that spread and migrate on a substrate. The
model has been tested successfully in experiments of epithelial
spreading and exhibits a morphological instability. It has beenshown to explain collective cell migration with an externallybroken symmetry (collective durotaxis). However, it remains
an interesting open question whether such a free-boundary
problem for tissues gives rise to spontaneous motion of cellcolonies solely driven by a morphological instability.

Carles Blanch-Mercader, Institut Curie
Morphogenesis of anisotropic cell monolayers: quantifying material properties by analyzing integer topological defects

Wed 16:15–18:15

Tissues made of anisotropic cells can exhibit features ofliquid crystals, such as long-ranged orientational order andtopological defects. During the development of organisms, suchfeatures often influence shape formation. However, the linkage
between geometry, topological defects and tissue mechanics
remains largely unexplored. First, I will show how we build on
the physics of liquid crystals to determine material parametersof cell monolayers. In particular, we use a hydrodynamical
description of a 2d active liquid crystal to study the steady-statemechanical patterns around integer topological defects. Thismodel predicts a transition from non-rotating asters to rotating
spirals. We apply our approach to spindle-shaped myoblast cellmonolayers in small circular confinements, which spontaneously
form isolated aster or spiral topological defects. Finally, I will
discuss how these findings can help one interpreting a secondarytransition from 2d cell monolayers to 3d multicellular structures,such as mounds or protrusions, and I will present some open
challenges in free-boundary models whereby couplings between
geometry and orientational order dominate. This is joint workwith P. Guillamat, A. Roux, K. Kruse. P. Guillamat and thepresenter contributed equally to this work.

Minisymposium
Wed 16:15–18:15 Room 3

Regularity of free boundaries (Part II)
Organizers: H. Shahgholian, M. Smit Vega Garcia

Mark Allen, Brigham Young University
Free Boundary Problem on a Cone
We consider a free boundary problem on cones depending
on a parameter c and study when the free boundary is allowed
to pass through the vertex of the cone. When the cone is
two-dimensional, the free boundary always avoids the vertexof the cone. However, when the cone is three-dimensional, thefree boundary may pass through the vertex of the cone if c issmall. For large values of c, the free boundary avoids the vertex.
Our result is analogous to a result of Morgan that classifies
when an area-minimizing surface on a cone passes through thevertex. This is joint work with Blake Barker, Jason Gardiner,and Mingyan Zhao.

Dennis Kriventsov, Rutgers University
Optimal regularity for an obstacle problem with log
singularity
I will present an optimal regularity result for solutions to thesemilinear equation∆u = (− log u+ )1{u>0} − (− log u− )1{u<0} .
In particular, solutions have log-Lipschitz derivatives. This
problem has similar structure to the classical two-phase obstacle
problem (and has the same blow-up limits), but the right-handside’s unfavorable monotonicity in u obstructs most argumentsfrom carrying over. The method I describe is based on a carefulanalysis of Weiss-type energies in this setting. This is basedon joint work with Henrik Shahgholian.

Edgard Pimentel, PUC-Rio
Nodal sets for elliptic equations in the double divergence form
We examine nodal sets for elliptic equations in the double
divergence form. We prove that the nondegenerate part of thenodal set inherits the regularity of the solutions. Then, we focus
on the structure of its singular part. Finally, we impose further
conditions on the coefficients and show that nodal sets do notdisconnect the domains. We end the talk with comments onfurther directions of research.

Murat Akman, University of Essex
An eigenvalue problem for p-Laplace equation with
an application to Minkowski type problem
We study existence and uniqueness of homogeneous solutions
to p-Laplace equation, p fixed, n − 1 < p < ∞, n ≥ 2, whenu is a solution in K(α) ⊂ Rn whereK(α) := {x = (x1 , . . . , xn ) : x1 > cos α |x|}
for fixed α ∈ (0, π], with continuous boundary value zero on∂K(α)\{0}. In our main result we show that if u has continuous
boundary value 0 on ∂K(π) then u is homogeneous of degree
1 − (n − 1)/p when p > n − 1. We then apply this result to
study the regularity of the Minkowski type problem.

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Thu 09:50–11:50
Minisymposium
Thu 09:50–11:50 Room 1

Asymptotic approaches to interface dynamics (Part I)
Organizers: J. José López Velázquez, J. KingJohn Ward, Loughborough University
Moving interfaces in a model of interacting mobile
and immobile bacterial populations
Bacteria typically exist in two phases, a mobile state (e.g.
swimming) or in a sessile state (forming colonies on solid-fluid
interfaces known as biofilms). The interaction and switching
between the mobile and immobile states can greatly influence
the rate of biofilm expansion, particularly in the early stages ofdevelopment. In this talk we discuss a simple model describing
biofilms as a growing viscous fluid on a surface in a static fluid
media consisting of swimming bacteria. Applying a thin-film
reduction, a coupled, two-phase system of PDEs is derived
consisting of Fisher’s type equations for the mobile cells andfor the biofilm; the latter consisting of a fourth-order diffusion
like term. The system generates a moving boundary problem
for the biofilm contact line. The key results will be presented,
in particular how the growth and diffusive properties of each of
the phases combine to affect the speed of the moving boundary.

melting a crystal dendrite. One major focus is the developmentof pinch-off singularities characterized by a blow-up of theinterface curvature and the bubble subsequently breaking up
into two. We show how similarity solutions can describe pinchoff, whereby the minimum radius behaves as a power law in timewith exponent 1/3 just before and after pinch-off has occurred.
For a geometry involving a cylindrical tube, there appears tobe time-dependent solutions that are like axially symmetric
Saffman-Taylor fingers or Taylor-Saffman bubbles. Further, iftime permits, I will also summarise some analysis for the related
problem of melting a crystal dendrite, including asymptotic
results in the limit that the dendrite melts completely.

I will discuss the general moving contact line problem, arisingfrom many fluid mechanics phenomena. The classical formulation of this model with the no-slip (Dirichlet) boundary condition for velocities at the liquid-solid interface gives rise to a
non-integrable singularity of the shear stress, which is known as
the “moving contact line paradox”. Y. Shikhmurzaev proposed(1993) a different approach to solve this issue. This approach,apart from the classical conservation equations, formulates theboundary conditions for the equations in the bulk phases inan elaborate way, which can be viewed as a generalizationof the existing models in the literature, although generated
from a different underlying theory. After giving an overview
of this model, I would like to derive a thin film approximationof Shikhmurzaev’s model to compare with the other solution
model of the contact line problem.

Diego Alonso Oran, Universität BonnAsymptotic shallow models arising in magnetohydrodynamics
In this talk, we derive new shallow asymptotic models for thefree boundary plasma-vacuum problem governed by the magnetohydrodynamic equations which are vital when describing largescale processes in flows of astrophysical plasma. More precisely,
we present the magnetic analogue of the 2D Green-Naghdi
equations for water waves in the presence of weakly sheared
vorticity and magnetic currents. Our method is inspired by ideas
for hydrodynamic flows to reduce the two/three-dimensional
dynamics of the problem to a finite cascade of equations which
can be closed at the precision of the model.

Scott McCue, Queensland University of Technology
Interfacial dynamics for axially symmetric Darcy flow
and related conduction limited melting problems
I will discuss a moving boundary model for the evolution ofan axially symmetric bubble of inviscid fluid in a homogeneous
porous medium otherwise saturated with a viscous fluid. The
model is a higher dimensional analog of Hele-Shaw flow, butalso applies for a one-phase quasi-steady Stefan problem for

Thu 09:50–11:50

Amrita Ghosh, Institute for Applied Mathematics, University of BonnOn Shikhmurzaev’s approach to the Contact Line
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Parallel Sessions Abstracts Thu 09:50–11:50

Minisymposium
Thu 09:50–11:50 Room 2

Stochastic free boundary problems (Part II)
Organizers: A. Djurdjevac, B. Gess, G. Grün

Peter Nejjar, Universität Bonn
Fluctuations of a microscopic shock wave in the Burgers equation
One of the most basic PDEs is the one-dimensional Burgers
equation. As is well known, this equation can be solved by themethod of characteristics. The asymmetric simple exclusion
process (ASEP) is an interacting particle system whose large
time particle density solves the Burgers equation. Furthermore,
ASEP provides a stochastic analogue to the charactersics: This
analogue is the second class particle. Second class particles
have proven invaluable to understand fluctuations in random
growth models belonging to the Kardar-Parisi-Zhang (KPZ)
universality class such as the KPZ equation. Here we consider
ASEP with a shock in the Burgers equation, and obtain thelarge time fluctuations of the second class particle following
the shock.

Benjamin Seeger, Université Paris - Dauphine
Scaling limits and homogenization of HamiltonJacobi equations with stochastic forcing
I will present results concerning the homogenization ofHamilton-Jacobi equations forced by stochastic and/or mixing
noise. Emphasis will be placed on the wide variety of possible
limiting problems that arise, depending on the scaling regime
and the structure of the equations. In particular, the effective
equation can be stochastic or deterministic, with the noise
having an enhancement effect in the latter case, or explosion
can occur. I also discuss some new regularity results, which are
an important tool in some of the proofs and are of independentinterest.

Ana Djurdjevac, Zuse Institute Berlin
PDEs and random fields on hypersurafaces with random velocity

Thu 12:45–14:45

The uncertainty in the mathematical modeling appears forvarious reasons, we are especially interested when it comes fromthe geometric aspect, i.e. curved domain. We study the PDEs
posed on curved domains that evolve with a given random
velocity. Utilizing the domain mapping method, we transfer the
problem into a PDE with random coefficients on a fixed domain.
For numerical analysis, we consider surface FEM coupled with
MC sampling. A natural question in this setting is how torepresent a random field on a hypersurface. We present theongoing work in this direction that is based on the wavelet
type expansion. This is a joint work with L. Church, C. Elliott,
M. Bachmayr.

Parallel Sessions Abstracts Thu 12:45–14:45

39

Thu 12:45–14:45
Minisymposium

Minisymposium
Thu 12:45–14:45 Room 2Freeboundary
problems
forhyperbolic/mixed-type PDEs (Part II)

nonlinear

Organizer: G.-Q. Chen

Mikhail Feldman, UW-Madison
Uniqueness and stability for shock reflection problem
We discuss shock reflection problem for compressible gas
dynamics, von Neumann conjectures on transition between
regular and Mach reflections, and existence of regular reflection
solutions for potential flow equation. Then we will talk about
recent results on uniqueness and stability of regular reflection
solutions for potential flow equation in a natural class of selfsimilar solutions. The approach is to reduce the shock reflection
problem to a free boundary problem for a nonlinear elliptic
equation, and prove uniqueness by a version of method ofcontinuity. A property of solutions important for the proof of
uniqueness is convexity of the free boundary. This talk is basedon joint works with G.-Q. Chen and W. Xiang.

Paolo Secchi, University of Brescia
Geometric optics for surface waves on the plasmavacuum interface
In this talk we consider the free boundary problem in threespace dimensions for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement, where the vacuum magnetic field obeys the div-curlsystem of pre-Maxwell dynamics, we do not neglect the displacement current in the vacuum region and consider the
Maxwell equations for electric and magnetic fields. Our aim is
to construct weakly nonlinear, highly oscillating solutions to thisplasma-vacuum interface problem. Under a necessary and sufficient stability condition for a piecewise constant backgroundstate, we construct by a geometric optics approach approximate solutions, at any arbitrarily large order of accuracy, when
the initial discontinuity displays high frequency oscillations. As
evidenced in earlier works, high frequency oscillations of theplasma-vacuum interface solution give rise to surface waves
on either side of the interface. Such waves decay exponentiallyin the normal direction to the interface and, in the weakly
nonlinear regime that we consider here, their leading amplitude
is governed by a nonlocal Hamilton-Jacobi type equation, as
for Rayleigh waves in elastodynamics and current-vortex sheets
in MHD. This is a joint work with Yuan Yuan (CAMIS, South
China Normal Univ.)

Dehua Wang, University of Pittsburgh
Inviscid limit of compressible viscoelastic equations
with the no-slip boundary condition
The inviscid limit for the two-dimensional compressible viscoelastic equations on the half plane is considered under the
no-slip boundary condition. It is well-known that for the corresponding inviscid limit of the compressible Navier–Stokes
equations with the no-slip boundary condition, one does notexpect the uniform energy estimates of solutions due to theappearance of strong boundary layers. Our results show thatthe deformation tensor plays an important role in the vanishing viscosity process and can prevent the formation of strong
boundary layers. This is a joint work with Feng Xie.

Steve Shkoller, University of California, Davist.b.a.
t.b.aFree boundary problems in cell biology (Part I)
Organizers: C. Gräser, M. Röger

Helmut Abels, Universität Regensburg
A Bulk-Surface Model for Lipid Raft Formation and
its Sharp Interface Limit
We discuss a model for phase separation on biological membranes for the evolution of lipid rafts which was recently proposed by Garcke, Rätz, Röger and Kampmann. The model isan extended Cahn–Hilliard equation which contains additionalterms to account for the active transport processes. We discuss
its sharp interface limit and existence of weak solutions for thelimit model.

Martin Burger, FAU Erlangen-Nürnberg
A Double Interface Model for Cell Blebbing
In this talk we will discuss the mathematical modelling of cell
blebbing phenomena, which is characterized by the interactionof two interfaces, the cell membrane and the actin cortex.
This is supplemented by a fluid structure interaction with
the intracellular flow and activation and deactivation of linker
proteins. We discuss sharp and diffuse interface models andtheir properties.

Luca Lussardi, Politecnico di Torino
Membrane shapes that minimize the multiphase
Canham-Helfrich energy
The Canham-Helfrich energy is widely used to describe
the elastic properties of biological membranes at the subcellular level. The membranes are modeled as surfaces in the
3-dimensional space and their shape minimize the energy which
penalizes the curvatures of the surface. This energy can begeneralized to the multiphase case in order to model also heterogeneous biological membranes. First of all I will review therotational symmetric case (Choksi-Morandotti-Veneroni, 2013).
If no symmetry of the minimizers is assumed, the problem
requires other tools. I will discuss existence of single and multiphase minimizers under area and enclosed volume constraints.
This is a joint work with K. Brazda and U. Stefanelli both from
University of Vienna.

Anna Logioti, University of BonnA free boundary problem modeling cell polarization
We study a model for cell polarization as a response to an
external signal which results in a system of PDEs for different
variants of a protein on the cell surface and interior respectively.
We study the evolution of this model for several reaction rates
on the membrane and the diffusion coefficient inside the cellbeing large. Under suitable scaling limits, solutions converge
to solutions of obstacle type problems, for which we show
uniqueness. Further, we prove the global stability of steadystates. For the steady states the occurrence of polarization has
been shown by Niethammer, Röger and Velázquez (2019) for
sufficiently small total mass of protein.

Thu 12:45–14:45

Thu 12:45–14:45 Room 1

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Parallel Sessions Abstracts Thu 12:45–14:45

Minisymposium
Thu 12:45–14:45 Room 3

Nonlocal free boundary problems (Part II)
Organizers: E. Valdinoci, J.-F. Rodrigues

Lisa Santos, University of Minho
On quasi-linear variational and quasi-variational inequalities with fractional gradient constraint
We extend the existence of generalized Lagrange multipliers
for the σ-gradient constrained problem for a class of quasi-linear
monotone operators obtained previously for stationary second
order linear operators involving the distributional Riesz fractional gradient. In the case of coercive quasi-linear operators,
using the continuous dependence of the variational inequality
solution, we also extend the existence of solutions to quasivariational inequalities when the threshold of the fractional
gradient constraint is given by a nonlocal operator depending
also on the solution. (Joint work with A. Azevedo and J.F.
Rodrigues)

Eduardo Teixeira, University of Central Florida
On a class of free boundary problems involving diffusion weights
I will discuss a class of free boundary problems ruled bysingular/degenerate diffusion operators and their connections
to nonlocal free boundary problems. Towards the end, I willreport how such geometric insights can be used to tackle issues
in the classical fully nonlinear regularity theory.

Catharine W.K. Lo, University of Lisbon
On a Class of Nonlocal Obstacle Type Problems
We consider one or two obstacles problems, and the N membranes problem for a non-symmetric Dirichlet form inconvex sets of H0s (Ω), 0 < s < 1. We extend several results,
such as the weak maximum principle, comparison properties,
approximation by bounded penalization, and also the LewyStampacchia inequalities. This provides regularity of the solutions, in L∞ (Ω) in the general case and local regularity in
2s,p
Wloc
(Ω) in the special case corresponding to the fractionals-Laplacian obstacle problem, which can be written with the
distributional Riesz fractional s-derivatives. The novel results
are complemented with the extension of the Lewy-Stampacchia
inequalities to the order dual of H0s (Ω) and some remarks on
the associated s-capacity and the s-nonlocal obstacle problem.
This is a joint work with J.-F. Rodrigues.

Harbir Antil, George Mason University
Approximation of Fractional Harmonic Maps

Thu 16:15–18:15

This talk addresses the approximation of fractional harmonic
maps. Besides a unit-length constraint, one has to tackle thedifficulty of nonlocality. We establish weak compactness results
for critical points of the fractional Dirichlet energy on unitlength vector fields. We devise and analyze numerical methods
for the approximation of various partial differential equations
related to fractional harmonic maps. The compactness results
imply the convergence of numerical approximations. Numerical examples on spin chain dynamics and point defects arepresented to demonstrate the effectiveness of the proposed
methods. This is a joint work with Soeren Bartels (Freiburg,
Germany) and Armin Schikorra (Pittsburgh, USA)

Parallel Sessions Abstracts Thu 16:15–18:15

41

Thu 16:15–18:15
Minisymposium
Thu 16:15–18:15 Room 2

FBP in the life sciences
Organizers: A. Friedman, L. Berlyand

Avner Friedman, The Ohio State University
A free boundary problem for fungal infection
Fungai are cells found in commensal residence, on skin andon mucosal surfaces of the human body, including the digestive tract, but some species are pathogenic. Fungal infection
may spread into deep-seated organs causing life-threatening
situations. Effective defense against fungal infection requires coordinated response by the innate and adaptive immune systems.
We represent the densities of the adaptive immune responseby neutrophils, N , the adaptive immune response by T cells,
T , and the fungal density by F , and introduce the following
parameters: A = density of N cells and B = density of T cells
in steady health state; a, b the strengths of the innate andadaptive immune systems, respectively, in response to fungal infection; and C = growth rate of fungai. Then J = aA+bB −C
represents the total balance of the immune response against
fungal infection. We developed a mathematical model of fungal infection consisting of a PDE system for (F, N.T ) in thefungal domains D(t), where the free boundary moves in thenormal direction n with velocity V (t) = h(−dF/dn) , whereh(s) is a linearly-bounded monotone increasing function. In
the radially-symmetric case, with D(t) = r < R(t) and freeboundary r = R(t), we prove global existence and uniqueness,with dR(t) > 0, and the following results: If J < 0 then R(t)remains bounded and F converge to 0 as t increases to infinity,
If J > 0 and R(t) increases to infinity as t increases to infinity
then (F, N, T ) converges to (F ∗, N ∗, T ∗) as t increases toinfinity If J > 0 and R(0) > R∗, then R(t) converges toinfinity as t increase to infinity The quantities F ∗, N ∗, T ∗ andR∗ are given explicitly by the parameters of the PDE system
This a joint work with King-Yeung Lam.

We consider a two-phase free boundary problem based ona simplified model of rheumatoid arthritis. In the model’ssimplified geometry, the free boundary is a function x=R(t)and the cartilage thickness is L-R(t). We prove global existence
and uniqueness of a solution, and derive qualitative properties ofthe free boundary. It is proved that the free boundary increases
in time, and the cartilage shrinks to zero as time approaches
infinity, even under treatment by a drug. It is also shown in the
reduced one-phased problem, with cartilage alone, that a larger
prescribed inflammation function leads to a faster destructionof the cartilage. This is joint work with Avner Friedman.

Tim Laux, University of BonnThe Hele-Shaw flow as the sharp-interface limit of
the Cahn–Hilliard equation with disparate mobilities
The Cahn–Hilliard equation is a well-studied phase-fieldmodel. In this talk, I will present a rigorous derivation of its
sharp-interface limit with a mobility function that degenerates
in one of the two phases. The proof is based on the interpretation of the PDE as a Wasserstein gradient flow. The limiting
PDE is the well-known Hele-Shaw flow, which governs theslow movement of the free boundary of a drop of water in the
narrow gap between two parallel horizontal plates. Our proof is
flexible enough to accommodate other effects such as external
forces. This is joint work with Milan Krömer (University ofBonn).

Atherosclerosis is a leading cause of death worldwide; it
originates from a plaque which builds up in the artery. We
considered a simplified model of plaque growth involving LDL
and HDL cholesterols, macrophages and foam cells, which
satisfy a coupled system of PDEs with a free boundary, theinterface between the plaque and the blood flow. In an earlier
work (with Avner Friedman and Wenrui Hao), we proved that
there exist small radially symmetric stationary plaques andestablished a sharp condition that ensures their stability. In ourrecent work (with Xinyue Zhao), we look for the existence of
non-radially symmetric stationary solutions. The absent of an
explicit radially symmetric stationary solution presents a big
challenge to verify the Crandall-Rabinowitz theorem; throughasymptotic expansion, we extend the analysis to establish afinite branch of symmetry-breaking stationary solutions which
bifurcate from the radially symmetric solutions. Since plaqueis unlikely to be strictly radially symmetric, our result would
be useful to explain the asymmetric shapes of plaque.

Adrian Lam, The Ohio State University
A free boundary problem of rheumatoid arthritis
Rheumatoid arthritis is an autoimmune disease characterized
by inflammation in the synovial fluid within the synovial joint
connecting two contiguous bony surfaces. The inflammation
diffuses into the cartilage adjacent to each of the bony surfaces,
resulting in their gradual destruction. The interface between the
cartilage and the synovial fluid is an evolving free boundary..

Thu 16:15–18:15

Bei Hu, University of Notre Dame
A Free Boundary Problem for modeling Plaques in
the Artery – Recent progress

42

Parallel Sessions Abstracts Thu 16:15–18:15

Contributed Session

Contributed Minisymposium
Thu 16:15–18:15 Room 1

Thu 16:15–18:15 Room 3

Geometric evolution of interfaces and transition layers(Part I)

Contributed session (Part IV)

Organizers: G. Wheeler, P. Rybka

Marco Morandotti, Politecnico di Torino
Analysis of a perturbed Cahn–Hilliard model for
Langmuir-Blodgett films
A one-dimensional evolution equation including a transportterm is considered; it models a process of thin films deposition.
Existence and uniqueness of solutions, together with continuous
dependence on the initial data and an energy equality are provedby combining a minimizing movement scheme with a fixedpoint argument. Finally, it is shown that, when the contributionof the transport term is small, the equation possesses a global
attractor and converges to a purely diffusive Cahn–Hilliard
equation. This is joint work with Marco Bonacini and Elisa
Davoli.

Danielle Hilhorst, CNRS and University Paris-Saclay
Singular limit for a stochastic Allen-Cahn equation
with nonlinear diffusion
We study a stochastic Allen-Cahn equation with nonlinear
diffusion and a mild random noise on a bounded domain in
Rn . We consider initial data that satisfy some non-degeneracy
conditions, and prove that steep transition layers develop withina very short time. We then study the motion of these transition
layers and derive a stochastic motion law for the sharp interface
limit. This is joint work with Perla El Kettani, Yong Joung
Kim and Hyunjoon Park.

Katarzyna Ryszewska, Warsaw University of Technology
A space-fractional Stefan problem
In this talk we will consider a non-local in space, one-phaseone-dimensional Stefan problem, where the diffusive flux takes
the form of the fractional Caputo derivative. The motivation
for studying such a problem originates from modelling the
diffusion and mass transport in heterogeneous media. A typicalexample of such phenomenon is a sub-surface water motion.
During the talk we will present the result concerning existenceof regular solution to this problem. The proof relies mainly on
analytic evolution operator theory and fixed point argument.

Mikołaj Sierżęga, University of Warsaw
Optimal Liouville theorem for a semilinear OrnsteinUhlenbeck equation

Thu 16:15–18:15

In their seminal 1985 paper Giga and Kohn analysed theblow-up behaviour of the subcritical Fujita equation through a
Liouville theorem for an associated elliptic equation of OrnsteinUhlenbeck type. In a subsquent work Giga provided a conditional extension of this Liouville theorem to a natural broader
class of semilinear Ornstein-Uhlenbeck equations and posed
a question of its unconditional validity, i.e. in the class ofbounded entire solutions. In this talk we will show that indeed
such a result holds. The key ingredient of the demonstration
relies on a generalisation of the Rellich-Pohozaev type argument which employs a family of special multipliers based on
Kummer functions. Even though the problem is posed on thewhole space this generalisation takes into account propertiesof the domain and provides a blueprint for analogous problems
involving boundaries.

Rolf Krause, USI - Università della Svizzera italiana
A recursive multilevel trust region method for phasefield models
We present and discuss non-linear multilevel methods for thenumerical solution of phase-field models for fracture. Phasefield models are computationally challenging due to large number of unknowns required for resolving the crack zone and theill conditioning caused by local changes in the damage variable.
We employ a recursive multilevel trust region method, which
combines global convergence with multigrid efficiency. A crucial
aspect is the design of level dependent objective functions, as
the underlying model relies on the mesh dependent parameters.
We introduce solution dependent objective functions that combine fine level description of the crack path with the coarse
level discretization. Numerical examples in are presented.

Irina Denisova, Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences
A problem governing the rotation of a two-phase
capillary liquid drop
We consider stability problem of a uniformly rotating liquidmass consisting of two viscous incompressible capillary selfgravitating liquids separated by a closed interface and bounded
outside by a free surface. The flow is governed by a freeboundary problem for the Navier–Stokes system with respect
to unknown perturbations of velocity vector field and pressurefunction. An additional condition is the fact that boundary
speed is equal to the normal velocity on the free boundaryand on the interface. We obtain unique solvability of a linear
problem, outline ways to prove the global solvability of thenonlinear problem provided that the initial data and the rotation
speed are small, as well as the proximity of unknown surfaces
to certain axisymmetric equilibrium figures.

Sebastian Aland, TU Freiberg
A combined sharp/diffuse interface approach for wetting of elastic substrates
The interaction of an elastic substrate with liquid droplets is
at small length scales dominated by surface tension forces. We
present a combination of a sharp and diffuse interface model tosimulate this scenario. The fluid-fluid interface is represented
by a diffuse layer to regularize the contact line singularity. The
solid-fluid interface is represented by a matched finite-element
grid and moved in the typical Arbitrary-Lagrangian-Eulerianway. As all equations are formulated in a Eulerian frame ofreference, we obtain a single momentum equation including
the solid and both fluid materials, which is very simple to solve
monolithically. We illustrate the numerical robustness of thisnovel method and compare it to the recent experimental andnumerical results.

Lucas Daniel Wittwer, HTW Dresden
Simulations of an active surface immersed in viscous
fluids
The surface of biological cells is connected to the cell cortex- a thin layer of active material. This layer exerts an active
contractile tension which regulates cellular shape by deforming
the surface. The strength of the active tension is controlled
by the concentration of force-generating molecules. Advective
transport of these molecules leads to a complex interplay of
surface deformation, hydrodynamics and molecule concentration which gives rise to pattern formation and self-organizedshape dynamics. In this talk, we present a numerical model toParallel Sessions Abstracts Thu 16:15–18:15

Contributed Session
Thu 16:15–18:15 Room 4

Contributed session (Part V)
Guozhi Dong, Humboldt-Universität zu Berlin
A class of second order geometric quasilinear hyperbolic PDEs and their application
We propose a class of novel second-order nonlinear hyperbolic PDEs inspired by the recent development of second-order
dynamics for accelerating the energy decay of gradient flows.
We put particular focus on a second-order total variation flow
and a second-order level set mean curvature flow, both with
damping terms weighted by some chosen parameters. We willshow some analytical results on the proposed equations, i.e.,
existence of solutions, uniqueness, and also some numericalaspects from the applications in imaging point of view, e.g.,denoising, correcting displacement errors. This is a joint workwith Michael Hintermueller and Ye Zhang.

Vladimir Vasilyev, Belgorod State National Research University
On Some Elliptic Boundary Value Problems in Canonical Domains
We study solutions of a boundary value problem for elliptica
pseudo-differential equation (Au)(x) = 0, x ∈ C+
, wheream
C+ is a certain cone in m-dimensional space R , with a certain
non-local additional condition. Using results and methods from
“Wave factorization of elliptic symbols, Kluwer Acad. Publ.,
2000” we study behavior of a solution for this problem undera → ∞, it corresponds to such case when two-dimensional conetransforms to a ray. Let us note that if a → 0, it corresponds
to the half-space Rm+ . The main conclusion is the following:
the boundary value problem has a limit under a → ∞ only if
the boundary function g(x1 ) satisfies certain functional onedimensional singular integral equation.

Seongmin Jeon, Purdue University
Almost minimizers for the thin obstacle problem withvariable coefficients
In this talk, we will consider almost minimizers for the thinobstacle problem with variable Hölder continuous coefficientsand zero thin obstacle, and discuss their regularity properties.
Under an additional assumption of quasisymmetry, we will establish the regularity of the regular set and a structural theoremon the singular set. The proofs are based on the generalizationof Weiss- and Almgren-type monotonicity formulas for almost
minimizers established earlier in the case of constant coefficients. This is joint work with Arshak Petrosyan and Mariana
Smit Vega Garcia.
Thu 16:15–18:15

simulate such an active viscous surface immersed in viscous fluids. We show the resulting patterning and cell shape dynamics
as well as the flow profiles in the two bulk phases and discuss
implications to the functioning of biological cells.

43

44

Parallel Sessions Abstracts Fri 09:50–11:50

Fri 09:50–11:50
Contributed Session

Contributed Minisymposium
Fri 09:50–11:50 Room 1

Fri 09:50–11:50 Room 2

Geometric evolution of interfaces and transition layers(Part II)

Contributed session (Part VI)

Organizers: G. Wheeler, P. Rybka

Glen Wheeler, University of Wollongong
On Chen’s flow
In this talk we quickly survey what is currently known for
Chen’s flow, and discuss some very recent results. Chen’s flowis the biharmonic heat flow for immersions, where the velocity
is given by the rough Laplacian of the mean curvature vector.
This operator is known as Chen’s biharmonic operator and thesolutions to the elliptic problem are called biharmonic submanifolds. The flow itself is very similar to the mean curvature flow
(this is essentially the content of Chen’s conjecture), however
proving this requires quite different strategies compared to themean curvature flow. We focus on new results available in low
dimensions - curves, surfaces, and 4-manifolds.

James McCoy, University of Newcastle
High order curvature flow of plane curves with generalised Neumann boundary conditions
We consider the parabolic polyharmonic diffusion and L2 gradient flows of the m-th arclength derivative of curvature forregular curves evolving with generalised Neumann boundary
conditions. In the polyharmonic case, we prove that if thecurvature of the initial curve is small in L2 , then the evolving
curve converges exponentially in the C ∞ topology to a straighthorizontal line segment. The same behaviour is shown for theL2 -gradient flow provided the energy of the initial curve issufficiently small. In each case the smallness conditions depend
only on m. This is joint work with Glen Wheeler and Yuhan
Wu.

Simon Blatt, Paris Lodron University Salzburg
On the Negative Gradient Flow of the p-Energy
This talk will be about ongoing work on the negative L2
gradient flow of p-elastic energies for curves. After an overview
over known results we will discuss short- and longtime existence
for these evolution equations using de Giorgi’s method ofminimizing movements. Apart from that the essential new toolin our approach is to write the evolving curves as approximate
normal graphs over a fixed smooth curves. In this way wecan prove a lower bound for the time of existence that only
depends on the W 2,p norm of the initial curve. We will shortly
discuss the pros and cons of this method and present someopen problems.

Piotr Rybka, University of Warsaw
A sixth order Cahn–Hilliard type equation with asmall deposition rate
We consider a one-dimensional sixth order Cahn–Hilliard
type equation describing the evolution of a growing crystalline
surface that undergoes faceting,
Fri 09:50–11:50

ut = δuux + ∆3 u − (u3 − u)xxxx
with periodic boundary conditions. This equation contains adestabilizing quadratic term corresponding to a deposition
rate. The well-posedness of this equation is known for periodic
boundary conditions. Existence of a global compact attractor
is also known. We study the case when the deposition rate issmall. We show that in this case the equation has a gradient
flow structure in an appropriate sense. Using this observation
we prove stabilization of solutions.

Enrico Valdinoci, University of Western Australia
The stickiness phenomenon for nonlocal minimal surfaces
We will present some recent results related to the boundary
behavior of nonlocal minimal surfaces, especially connected withboundary discontinuities, stickiness to the reference domain,
yin-yang results, multiplicity of minimizers, and topologicalchanges.

Subas Acharya, University of Texas at Dallas
Free Boundary Problem with Real Options
We consider a Free Boundary Problem (FBP) associated witha real options problem. The real options problem is posed as astochastic optimal control problem. The investment strategy(control), involves a one-time option to expand and a one-time
option to terminate the project. The timing and amount of
the investment are parameters to be optimized to maximize
the profit. This stochastic optimization problem is reduced toa variational inequality (VI) and then to a FBP for a PDE. We
use a specific substitution for the value function to reduce thePDE into a FBP for ODE. The focus of this work is on deriving
sufficient conditions for solvability of the VI and providing
a characterization of the solution (the value function), for ageneral form of the nonlinear investment cost.

Xin Liu, Weierstrass InstituteSecond law of thermodynamics and bounded entropy
solutions in the compressible Navier–Stokes system
Our goal is to investigate the existence of global-in-time
solutions with bounded entropy to the compressible Navier–Stokes system. Previous study of Cauchy problems motivates
the free boundary problem, where the flows connect to vacuumwith continuous density on the moving boundary. We mainly
focus on the spherically symmetric solutions. Two results will
be presented. 1. Global solutions to isentropic flows with orwithout density jump on the moving boundary; 2. A class of
self-similar solutions are presented, and the bounded entropy
solutions are obtained with initial data perturbed around suchself-similar data.

Yvonne Stokes, University of Adelaide
Asymptotic modelling of drawing of micro-structured
optical fibres
An efficient asymptotic model for the drawing of fibres with
arbitrary cross-sectional geometry will be described. ODEs
describe the change in area of the cross-section and the temperature from preform to fibre. In general, these are coupledwith a 2D transverse-flow problem describing the evolution of
the geometry in the cross-section due to surface tension andpressure. The accuracy of the model will be demonstrated bycomparison with experiments and finite-element simulations.

Parallel Sessions Abstracts Fri 12:45–14:45

45

Fri 12:45–14:45
Minisymposium

Minisymposium
Fri 12:45–14:45 Room 1

Fri 12:45–14:45 Room 2Free boundary problems in cell biology (Part II)

Surface PDEs (Part II)

Organizers: C. Gräser, M. Röger

Organizers: C. Venkataraman, T. Ranner

Chandrasekhar Venkataraman, University of Sussex
Multiscale modelling, analysis and simulation of cellsignalling processes

Axel Voigt, TU Dresden
Fluid deformable surfaces - a numerical approach bysurface FEM

We consider homogenisation of a model for cell signalling
processes in biological tissues. Such signalling processes are
the primary mechanism by which cells interact and respondto external stimuli. Hence they play an important role in the
majority of cell biological phenomena. The signalling model
we consider includes diffusion and nonlinear reactions on thecell surfaces, and both inter- and intracellular signalling. We
derive, under the assumption of a periodic cell distribution,
the equations satisfied in the limit as the cell number tends toinfinity with the volume fraction of tissue occupied by the cells
constant. Furthermore, we present a finite element method
for the limiting two-scale bulk surface system and report on
numerical simulations of the model equations.

Lipid membranes are examples of fluid deformable surfaces.
They can be viewed as two-dimensional viscous fluids withbending elasticity. With this solid-fluid duality any shape change
contributes to tangential flow and vice versa any tangential
flow on a curved surface induces shape deformations. This tightcoupling between shape and flow makes curvature a naturalelement of the governing equations. We derive the governing
equations as a thin-film limit of a generalized Navier–Stokes
equation, propose a numerical approach by finite elements
and show numerical results, which can serve as benchmark
problems.

We consider a hybrid model of a biomembrane with attachedproteins. We investigate the arrangement of proteins withrespect to membrane mediated interactions. The membraneis represented by a near-spherical or near-tubular surface andproteins by rigid bodies which attach to the membrane at
finitely many points. The model is based on tractable quadraticenergies which are perturbations of the Canham-Helfrich energy
with point constraints. Well-posedness of the minimisation
problem for the shape of the membrane and finite element
approximations will be described. We prove differentiability ofthis energy with respect to the location of attached particles
and give a formula for the derivative. Results will be illustrated
by numerical experiments. Joint work with C.M. Elliott and C.
GräserDiane Peurichard, Inria Paris
Multi-scale approach for a model of tumor growth:from short-range repulsion to Hele-Shaw problems
In this talk, we investigate the multi-scale link for a model oftumor growth. We start from a microscopic model where cells
are modelled as 2D spheres undergoing short range repulsion
and cell division. We derive the associated macroscopic dynamics leading to a porous media type equation. As the macroscopic equation obtained through usual derivation method fails
at providing the correct qualitative behavior, we propose amodified version of the macroscopic equation introducing adensity threshold for the repulsion. We numerically validate the
new formulation by comparing the solutions of the micro- andmacro- dynamics. Moreover, we study the asymptotic behaviorof the dynamics as the repulsion between cells becomes singular (leading to non-overlapping constraints in the microscopic
model)In this talk I will present a new semi-discrete finite element
scheme for the evolution of three parametrised curves that areconnected by a triple junction and move by curvature flow.
At the triple junction conditions are imposed on the angles
at which the curves meets. I will provide ideas underlying theconvergence analysis and show some numerical tests. This is
joint work with B. Stinner.

Balázs Kovács, University of Regensburg
A convergent evolving finite element algorithm forWillmore flow of closed surfaces
We will sketch a proof of convergence for a finite element
semi-discretisation of Willmore flow of closed two-dimensionalsurfaces. As our algorithm for mean curvature flow, the proposed method discretizes evolution equations for the normal
vector and mean curvature, together with the velocity law.
This numerical method admits a convergence analysis, which
combines stability estimates and consistency estimates to yield
optimal-order H 1 -norm semi-discrete error bounds. The stability analysis is based on the matrix-vector formulation of thefinite element method and does not use geometric arguments.
Stability is proven using a non-standard version of energy estimates, which we will sketch during the talk. We will alsopresent various numerical experiments.

Matthias Röger, TU Dortmund
A bulk-surface Gierer-Meinhardt model
We consider a coupled system of a diffusion equation in
a volume coupled to a Gierer-Meinhardt type system on theboundary. We prove existence of solutions and present numerical simulations.

Fri 12:45–14:45

Philip Herbert, University of Koblenz-Landau
Surface PDE models for membrane mediated particle interactions on near-spherical or near-tubular
biomembranes

Paola Pozzi, University of Duisburg-Essen
On a converging FE-scheme for motion by curvatureof a network with a triple junction.

46

Parallel Sessions Abstracts Fri 12:45–14:45

Minisymposium
Fri 12:45–14:45 Room 3

Asymptotic approaches(Part II)

tointerface dynamics

Organizers: J. José López Velázquez, J. King

Jonas Jansen, Universität Bonn
Homogenisation of a nonlinear Poisson equation in
perforated domains and a free-boundary problem
One important problem in homogenisation is to describe aneffective theory for electric charges in a material with many tinyholes or the flow of a fluid around (potentially moving) particles.
To obtain such a theory, one considers randomly distributed
holes and sends the number of holes to infinity. Depending on
the scaling behaviour of the radii of the holes, one obtains different deterministic limiting equations, including - in the linear
case - the famous Cioranescu-Murat limit. In this talk, I will
discuss homogenisation phenomena of the nonlinear equation−∆um + λm |um |p−1 um = 0 in a perforated domain in thethree-dimensional torus with deterministic Dirichlet boundary
conditions on the holes. I will discuss different scaling limits andshow how a free-boundary problem arises as homogenisation
limit.

Mark Blyth, University of East Anglia
Asymptotic solutions for free-surface flow over localised topography
Steady free-surface flow over a localised bottom topography is examined at critical Froude number (F = 1). In thiscase the forced KdV equation that applies for small amplitude
topography reduces to the inhomogeneous nonlinear ordinary
differential equation for the free-surface disturbance u(x),u00 + u2 = αf (x),where α is a parameter. The rate of decay of the forcing
function f (x) in the far field is important and it has a strong
influence on the structure of the solution space. Numericalcalculations for a Gaussian forcing, with exponential far-fielddecay, suggest that there exists an infinite number of distinct
solution branches each of which terminates at some valueof α. We provide an asymptotic description of the solution
valid for large α on any given branch following a standard
boundary-layer type of approach augmented by a method forglueing homoclinic connections. We also present a general
asymptotic description of the solutions near to a termination
point.. Solutions for topographies whose solution branches do
not terminate, including a Lorentzian forcing, will also be briefly
discussed.

Linda Cummings, New Jersey Institute of Technology
Asymptotic thermal modeling of droplet assembly innanoscale molten metal films

Fri 12:45–14:45

We consider a thin metal film on a thermally conductive
substrate exposed to an external heat source in a setup where
the heat absorption depends on the local film thickness. Our
focus is on modeling film evolution while the film is molten.
The film geometry modifies local heat flow, which in turn may
influence the film surface evolution through thermal variationof material properties. We use asymptotic analysis to developa thermal model that is accurate, computationally efficient,and that accounts for the heat flow in both the in-plane andout-of-plane directions. We apply this model to describe metal
films of nanoscale thickness exposed to heating and melting
by laser pulses, a setup commonly used for self and directedassembly of various metal geometries via dewetting while thefilms are in the liquid phase. We find that thermal effects
play an important role, and in particular that the inclusionof temperature dependence in the metal viscosity modifies
the time scale of the evolution significantly. The thickness,thermal conductivity, and rate of heat loss of the underlying
substrate are shown to be crucial in accurately modeling film
temperatures and subsequent phase changes in the film. Since
in many cases the substrate cools the film, modifications to thesubstrate temperature may induce different dewetting speeds
via temperature dependent viscosity of the film. We show via
3D GPU simulations that this may result in various frozen film
patterns since full dewetting may not occur while the film is in
the liquid phase. This research was supported by NSF CBET1604351, NSF-DMS-1815613 and by CNMS2020-A-00110.

Index of Authors

47

Index of Authors
Abels, Helmut, Universität Regensburg
p. 39
14:15
Thu
Room 2Acharya, Subas, University of Texas at Dallas
p. 44
10:20
Fri
Room 2
Akman, Murat, University of Essex
p. 36
16:15
Wed
Room 3Aland, Sebastian, TU Freiberg
p. 42
16:15
Thu
Room 3
Alert, Ricard, Princeton University
p. 35
17:15
Wed
Room 2
Allen, Mark, Brigham Young University
p. 36
16:45
Wed
Room 3Alonso Oran, Diego, Universität Bonn
p. 37
10:50
Thu
Room 1
Antil, Harbir, George Mason University
p. 40
13:45
Thu
Room 3
Arroyo, Marino, Universitat Politecnica de CatalunyaBarcelonaTech
p. 29
10:50
Wed
Room 1Bae, Myoungjean, KAIST
p. 22
10:20
Tue
Room 3Banas, Lubomir, Bielefeld University
p. 30
11:20
Wed
Room 3
Baran, Björn, Max Planck Institute for Dynamics of Complex
Technical Systems, Magdeburg
p. 33
13:45
Wed
Room 3
Bartels, Sören, University of Freiburg
p. 25
17:05
Tue
Room 1Plenary
p. 14
9:00
Wed
Berlyand, Leonid, Penn State University
p. 35
16:15
Wed
Room 2
Bertozzi, Andrea, UCLA math department
Plenary
p. 16
18:20
Thu
Blanch-Mercader, Carles, Institut Curie
p. 36
16:45
Wed
Room 2
Blatt, Simon, Paris Lodron University Salzburg
p. 44
11:20
Fri
Room 1
Blyth, Mark, University of East Anglia
p. 46
13:15
Fri
Room 3
Bonito, Andrea, Texas A&M University
p. 25
17:35
Tue
Room 1
Bothe, Dieter, TU Darmstadt
p. 21
10:50
Tue
Room 2
Brandner, Philip, RWTH Aachen University
p. 29
10:20
Wed
Room 1
Bronsard, Lia, McMaster University
Plenary
p. 14
15:00
Tue
Burger, Martin, FAU Erlangen-Nürnberg
p. 39
13:15
Thu
Room 2
Buttazzo, Giuseppe, University of Pisa
p. 20
12:45
Mon Room 1
Caetano, Diogo, University of Warwick
p. 26
18:05
Tue
Room 2
Casademunt, Jaume, University of Barcelona
p. 35
17:45
Wed
Room 2Chambolle, Antonin, CNRS and CEREMADE, Université ParisDauphine, PSL, France
p. 12
9:00
Mon Plenary
p. 35
17:15
Wed
Room 1
Chernov, Alexey, University of Oldenburg
p. 24
13:15
Tue
Room 2Colli, Pierluigi, University of Pavia
p. 20
13:45
Mon Room 2
Cummings, Linda, New Jersey Institute of Technology
p. 46
13:45
Fri
Room 3
Deckelnick, Klaus, Otto-von-Guericke-Universität Magdeburg
p. 20
13:15
Mon Room 2
p. 35
16:15
Wed
Room 1

Denisova, Irina, Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences
p. 42
17:15
Thu
Room 3Dirr, Nicolas, Cardiff University
p. 30
10:20
Wed
Room 3
Djurdjevac, Ana, Zuse Institute Berlin
p. 38
10:20
Thu
Room 2
Dong, Guozhi, Humboldt-Universität zu Berlin
p. 43
16:45
Thu
Room 4Du, Qiang, Columbia University
Plenary
p. 15
15:00
Wed
Eberle, Simon, University of Duisburg-Essen
p. 32
14:15
Wed
Room 1
Edelmann, Dominik, Eberhard Karls Universität Tübingen
p. 27
17:35
Tue
Room 3
Feldman, Mikhail, UW-Madison
p. 39
13:45
Thu
Room 1
Fernández-Real, Xavier, EPFL
p. 29
10:20
Wed
Room 2
Figalli, Alessio, ETH-Bereich Hochschulen
Plenary
p. 16
15:00
Thu
Fonseca, Irene, Carnegie Mellon University
p. 12
15:00
Mon Plenary
Friedman, Avner, The Ohio State University
p. 41
16:15
Thu
Room 2Gahn, Markus, University of Heidelberg - Interdisciplinary
Center for Scientific Computing (IWR)
p. 19
10:50
Mon Room 3
Garcke, Harald, Universität Regensburg
p. 23
14:15
Tue
Room 1Geiersbach, Caroline, Weierstrass Institute
p. 24
12:45
Tue
Room 2
Ghosh, Amrita, Institute for Applied Mathematics, Universityof Bonn
p. 37
10:20
Thu
Room 1
Giorgini, Andrea, Indiana University
p. 34
13:45
Wed
Room 4
Grasselli, Maurizio, Politecnico di Milano
p. 20
14:15
Mon Room 2
p. 34
13:15
Wed
Room 4
Grillmeier,
Hubertus,Friedrich-Alexander-Universität
Erlangen-Nürnberg
p. 30
9:50
Wed
Room 3
Ha, Kyung, UCLA math department
p. 28
18:05
Tue
Room 4
Harbrecht, Helmut, University of Basel
p. 24
14:15
Tue
Room 2Hardering, Hanne, TU Dresden
p. 35
16:45
Wed
Room 1
Hensel, Sebastian, Institute of Science and Technology Austria
(IST)
p. 30
10:50
Wed
Room 3
Herbert, Philip, University of Koblenz-Landau
p. 45
12:45
Fri
Room 1
Hilhorst, Danielle, CNRS and University Paris-Saclay
p. 42
16:45
Thu
Room 1
Hinze, Michael, Universität Koblenz-Landau
p. 20
12:45
Mon Room 2
Hu, Bei, University of Notre Dame
p. 41
17:15
Thu
Room 2
Jansen, Jonas, Universität Bonn
p. 46
12:45
Fri
Room 3
Jeon, Seongmin, Purdue University
p. 43
16:15
Thu
Room 4
Kahle, Christian, Universität Koblenz-Landau
p. 19
10:20
Mon Room 2
Karakhanyan, Aram, University of Edinburgh
p. 29
10:50
Wed
Room 2

48

Index of Authors

Keil, Tobias, Weierstrass Institute
p. 19
10:50
Mon Room 2
Khatiashvili, Nino, Iv. Javakhishvili Tbilisi State University
p. 28
17:05
Tue
Room 4
Kim, Sunghan, KTH Royal Institute of Technology
p. 32
13:15
Wed
Room 1
Knopf, Patrik, Universität Regensburg
p. 33
12:45
Wed
Room 3
Knüpfer, Hans, Universität Heidelberg
p. 21
10:20
Tue
Room 2
Koiso, Miyuki, Kyushu University
p. 21
10:20
Tue
Room 1
Kovács, Balázs, University of Regensburg
p. 45
14:15
Fri
Room 2
Krause, Rolf, USI - Università della Svizzera italiana
p. 42
17:45
Thu
Room 3
Kriventsov, Dennis, Rutgers University
p. 36
17:15
Wed
Room 3Kumazaki, Kota, Nagasaki University
p. 27
18:05
Tue
Room 3Lam, Adrian, The Ohio State University
p. 41
16:45
Thu
Room 2
Lam, Kei Fong, Hong Kong Baptist University
p. 19
9:50
Mon Room 2
Laurençot, Philippe, University of Toulouse
p. 21
11:20
Tue
Room 2
Laux, Tim, University of Bonn
p. 41
17:45
Thu
Room 2
Li, Wenbo, University of Tennessee, Knoxville
p. 25
18:05
Tue
Room 1
Lienstromberg, Christina, University of Bonn
p. 18
10:20
Mon Room 1
Liu, Xin, Weierstrass Institute
p. 44
9:50
Fri
Room 2
Lo, Catharine W.K., University of Lisbon
p. 40
14:15
Thu
Room 3
Logioti, Anna, University of Bonn
p. 39
13:45
Thu
Room 2
Lussardi, Luca, Politecnico di Torino
p. 39
12:45
Thu
Room 2
Marveggio, Alice, Institute of Science and Technology Austria
(IST)
p. 26
18:35
Tue
Room 2Massing, André [canceled], Norwegian University of Scienceand Technology
p. 19
10:20
Mon Room 3
McCoy, James, University of Newcastle
p. 44
10:20
Fri
Room 1
McCue, Scott, Queensland University of Technology
p. 37
11:20
Thu
Room 1
Metzger, Stefan, FAU Erlangen-Nürnberg
p. 32
13:45
Wed
Room 2
Miura, Tatsuya, Tokyo Institute of Technology
p. 21
9:50
Tue
Room 1
Morandotti, Marco, Politecnico di Torino
p. 42
17:15
Thu
Room 1
Mucha, Piotr B., University of Warsaw
p. 18
11:20
Mon Room 1
Nazarov, Alexander, St. Petersburg Dept of Steklov Instituteand St. Petersburg State University
p. 29
9:50
Wed
Room 2
Nejjar, Peter, Universität Bonn
p. 38
9:50
Thu
Room 2
Niethammer, Barbara, University of Bonn
Plenary
p. 15
9:00
Thu
Nürnberg, Robert, University of Trento
p. 32
14:15
Wed
Room 2
Okumura, Makoto, Hokkaido University

p. 26
17:35
Tue
Room 2Oudet, Edouard, Université Grenoble Alpes
p. 20
13:15
Mon Room 1
Park, Hyangdong, Yonsei University
p. 22
11:20
Tue
Room 3
Park, Jinwan, Seoul National University
p. 32
12:45
Wed
Room 1Peschka, Dirk, Weierstrass-Institut für Angewandte Analysis
und Stochastik
p. 19
9:50
Mon Room 3
Petras, Argyrios, Johann Radon Institute for Computationaland Applied Mathematics (RICAM)
p. 29
9:50
Wed
Room 1
Peurichard, Diane, Inria Paris
p. 45
13:45
Fri
Room 1
Pimentel, Edgard, PUC-Rio
p. 36
17:45
Wed
Room 3
Pinnau, René [canceled], TU Kaiserslautern
p. 33
14:15
Wed
Room 3
Pozzi, Paola, University of Duisburg-Essen
p. 31
9:50
Wed
Room 4
p. 45
13:45
Fri
Room 2
Pukhnachev, Vladislav, Lavrentyev Institute of Hydrodynamics
p. 28
17:35
Tue
Room 4Ranner, Thomas, University of Leeds
p. 32
13:15
Wed
Room 2
Rocca, Elisabetta, University of Pavia
p. 18
9:50
Mon Room 1
Röger, Matthias, TU Dortmund
p. 45
13:15
Fri
Room 2
Ros-Oton, Xavier, ICREA & Universitat de Barcelona
Plenary
p. 17
15:00
Fri
Rumpf, Martin, Universität Bonn
p. 35
17:45
Wed
Room 1
Rybka, Piotr, University of Warsaw
p. 44
9:50
Fri
Room 1
Ryszewska, Katarzyna, Warsaw University of Technology
p. 42
16:15
Thu
Room 1
Santos, Lisa, University of Minho
p. 40
12:45
Thu
Room 3
Saye, Robert, Lawrence Berkeley National Laboratory
p. 13
16:15
Mon Plenary
Scardia, Lucia, Heriot-Watt University
p. 31
11:20
Wed
Room 4
Scarpa, Luca, Politecnico di Milano
p. 23
12:45
Tue
Room 1
Schmidt, Alfred, University of Bremen
p. 32
12:45
Wed
Room 2
Secchi, Paolo, University of Brescia
p. 39
12:45
Thu
Room 1
Seeger, Benjamin, Université Paris - Dauphine
p. 38
10:50
Thu
Room 2
Shkoller, Steve, University of California, Davis
p. 39
14:15
Thu
Room 1Sierżęga, Mikołaj, University of Warsaw
p. 42
17:45
Thu
Room 1
Soave, Nicola, Politecnico di Milano
p. 32
13:45
Wed
Room 1
Stefanelli, Ulisse, University of Vienna
p. 31
10:50
Wed
Room 4
Stinner, Björn, University of Warwick
p. 23
13:15
Tue
Room 1
Stokes, Yvonne, University of Adelaide
p. 44
10:50
Fri
Room 2
Strelnikov, Dmytro, TU Ilmenau
p. 33
13:15
Wed
Room 3Stylianou, Athanasios, Universität Kassel
p. 28
18:35
Tue
Room 4

Index of Authors

Teixeira, Eduardo, University of Central Florida
p. 40
13:15
Thu
Room 3
Thomas, Marita, Weierstrass Institute for Applied Analysis
and Stochastics
p. 23
13:45
Tue
Room 1
Tice, Ian, Carnegie Mellon University
p. 34
12:45
Wed
Room 4
Tonegawa, Yoshihiro, Tokyo Institute of Technology
Plenary
p. 13
9:00
Tue
Tucsnak, Marius, University of Bordeaux
p. 18
10:50
Mon Room 1
Valdinoci, Enrico, University of Western Australia
p. 21
10:50
Tue
Room 1
p. 44
11:20
Fri
Room 2
Vasilyev, Vladimir, Belgorod State National Research University
p. 43
17:15
Thu
Room 4
Vázquez, Juan Luis, Universidad Autónoma de Madrid
p. 29
11:20
Wed
Room 2Velichkov, Bozhidar, University of Naples Federico II
p. 20
13:45
Mon Room 1
Venkataraman, Chandrasekhar, University of Sussex
p. 45
13:15
Fri
Room 1
Voigt, Axel, TU Dresden
p. 45
12:45
Fri
Room 2von Wolff, Lars, University of Stuttgart
p. 26
17:05
Tue
Room 2
Walker, Shawn, Louisiana State University
p. 25
18:35
Tue
Room 1
Wang, Dehua, University of Pittsburgh
p. 39
13:15
Thu
Room 1
Wang, Tao, Wuhan University
p. 22
10:50
Tue
Room 3
Ward, John, Loughborough University
p. 37
9:50
Thu
Room 1
Weiser, Martin, Zuse Institute Berlin
p. 27
18:35
Tue
Room 3Wheeler, Glen, University of Wollongong
p. 44
10:50
Fri
Room 1
Wilke, Mathias, Martin-Luther University Halle-Wittenberg
p. 31
10:20
Wed
Room 4
Wittwer, Lucas Daniel, HTW Dresden
p. 42
16:45
Thu
Room 3Wu, Hao [canceled], Fudan University
p. 21
9:50
Tue
Room 2
Wulbusch, Nick, University of Oldenburg
p. 24
13:45
Tue
Room 2
Xiang, Wei, City University of Hong Kong
p. 22
9:50
Tue
Room 3Zhao, Xinyue, University of Notre Dame
p. 27
17:05
Tue
Room 3
Zuazua, Enrique, Friedrich-Alexander-Universität ErlangenNürnberg
Plenary
p. 17
9:00
Fri

49