数理解析研究所講究録 1330

反応拡散方程式系に現れる動的パターンの解析とその周辺

onference
onDynamics of Patterns in Reaction-Diffusion Systems
and the Related Topics

京都大学数理解析研究所

2003 年 7 月

Preface

Reaction-d 垣干 usion systems well describe large diversity of complex spatio-as spiral or
temporal patterns occuring in reacting and diffusing media
target pattens of chemical waves, propagating pukes in nerve system and spiky
patterns in morphogenesis and so on, which have been discussed from theoreticaland complementarily numerical points of view. Specialy, the structure of stationary solutions including traveling waves have been extensively investigated
together with the stabilty and the bifurcation structure. And quite reoently,
detail informations on the properties of solutions not only in such static states
but also in dynamic states have been revealed. By using the informations, we
can understand much more complex dynamics of solutions theoreticffiy such as$\mathrm{s}\mathrm{u}\mathrm{A}$coUision of pulses and interaction of interfaces.
In the conference, recent theoretical approaches to deal with various dynamical motion in reaction-diffusion systems and the related topics were discussed.
This proceeding contains acollection of the papers related to the thema ofthe conference. The individual authors of this book were participants of theconference.
We hope that the results reported in the conference will contribute to future
researches on the subject.
Finally, we would like to thank all of the contributors in this conference. Ako
we thank Grand-in-Aid for Scientific Researches, $\mathrm{A}(1)12304006,$ $\mathrm{C}(2)12640217$ ,$\mathrm{C}(2)$13640107.
S.-I. Ei (Yokohama City University)
H. lkeda (Toyama University)
M. Mimura (Hiroshima University)

June 2003

反応拡散方程式系に現れる動的パターンの解析とその周辺
Conference

onDynamics of Patterns in Reaction-Diffusion Systems
and the Related Topics
Organizers: Shin-Ichiro , Hideo IKEDA and Masayasu MIMURA
November 25th (Monday)-November 28th (Thursday), 2002
Room 420, RIMS Kyoto University, Kyoto, Japan$\mathrm{E}\mathrm{I}$

Program25th Nov. (Mon)
13:20-13:30 Opening address Shin-Ichiro Ei (Yokohama City University)
13:30- 14:10 Ycsumasa Nishiura (Hokkaido University)
Strong interactions among particle like solutions in dissipative systems
14:20- 15:00 Michiel Bertsch (CNR and University of Rome )Director fields and their evolution
15:20- 16:00 Yoshihisa Morita (Ryukoku University)
Stable solutions to the Ginzburg-Landau equation in athin domain
16:10- 16:50 Rustum Choksi (Simon Fraser University)
Mathematical Aspects of Microphase Separation of Diblock Copolymers$\mathrm{I}\mathrm{I}$26th Nov. (Tue))
10:00- 10:40 Ken-Ichi Nakamura (University ofBounds for effective speeds of traveling fronts in spatially periodic media
11:00- 11:40 Rancois Hamel (Universite Aix-Marseille III)
Conical-shaped travelhng ffonts and afree boundary problem
arising in combustion theory$\mathrm{E}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\alpha \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}$11:40- 13:30 Lunch break
13:30- 14:10 Tasso J. Kaper (Boston University)
Pulse dynaics: self-replication and fimite time blowup
14:20- 15:00 Tsutomu Ikeda (Ryukoku University)
Bifurcation of helical wave ffom traveling wave
15:20- 16:00 Jong-Shenq Guo (National Taiwan Normal University)
Traveling waves for discrete quasilinear monostable dynamics
16:10-16:50 Izumi Takagi (Tohoku University)
Patterns generated by an activator-inhibitor system in avery thin domair

Nov. (Wed)10:40 Dongho Chae (Seoul National University)
On the incompressible Euler system and its perturbations
11:00- 11:40 Tonia Ricciardi (Federico University of Naples)
Anonlinear elliptic system from Maxwell-Chern-Simons vortex theory$27\mathrm{t}_{[perp] 1}^{1}$$10\cdot.00-$$\mathrm{I}\mathrm{I}$11:40-13:30 Lunch break
13:30- 14:10 Eiji Yanagida (Tohoku University)
Behavior of solutions for a supercritical semilinear heat equation
14:20- 15:00 Takao Ohta (Hiroshima University)
Oscillations of Phase Separated Domains in Reactive Mixtures
15:20- 16:00 Cyffi. Muratov (New Jersey Institute of Technology)
Free boundary problem and its applications to reaction-diffusion systemsof activator-inhibitor type16:10- 16:50 Tohru Tsujikawa (Miyazaki University)
model
Singular limit analysis of aggregating pattems in$\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{m}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{x}\mathrm{i}_{\mathrm{S}-\Psi}\mathrm{o}\mathrm{w}\mathrm{t}\mathrm{h}$28th Nov. (Thu)
Vergata ”)
Passo (Universita’ Roma ”
10:00- 10:40 Roberta
Operators of Thin-Film tyPe: qualitative properties and open problems
11:00- 11:40 Kunimochi Sakamoto (Hiroshima University)
An approximation of reaction-diffusion systems by interface equations
coupled with aparabolic or elliptic equation
Closing address
lL40$\mathrm{D}\mathrm{a}1$$\mathrm{d}\mathrm{i}$$\mathrm{T}\mathrm{o}\mathrm{r}$反応拡散方程式系に現れる動的パターンの解析とその周辺
Conferenceon
Dynamics of Patterns in Reaction-Diffusion Systems
and the Related Topics
研究集会報告集

2002 年 11 月 25 日 \sim 1 1 月 28 日
栄伸一郎 (Shin-Ichiro Ei)
Ikeda)
池田 条雄

研究代表者
副代表者

$\omega.\mathrm{d}\omega$

三村”

昌泰 (Maswasu Min$\mathrm{u}\mathrm{r}\mathrm{a}$)目次

1
1. Remmks on ffie Perturbed Euler equations
Dongho Chae
National Univ.
10
Copolymers
of Diblock Copolymers————–of Microphase
2. Mathematicg1
Rustum Choksi
Simon Fraser Univ.
3. TRAVELING WAVES FOR DISCRETE QUASILINEAR MONOSTABLE
DYNAMICS $——————————————–\cdot\cdot----------\sim-------------- 18$
Jong-Shenq Guo
National Taiwan Normal Univ.
-diffiion equations ———-25
4. Conical-shaped ffavelling ffonts in someFrancois Hamel
Univ. Aix-Marseille$\mathrm{S}\infty \mathrm{u}1$$\mathrm{S}\mathrm{e}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\dot{\mathrm{h}}\mathrm{o}\mathrm{n}$$\mathrm{A}\mathrm{s}\mathrm{p}\infty \mathrm{t}\mathrm{s}$$\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\dot{\mathrm{h}}\mathrm{o}\mathrm{n}$$\mathrm{e}\mathrm{d}$$\mathrm{m}$wave
5. Bifilrcation of helical wave fiom ffaveling wave—————————————40

6.
5. Stable

龍谷大・理工池田勉 (Tsubmu Ikeda)

京大・数理研長山

雅晴 (Masaham N 昭町 ma)

富山大・理池田 条雄 (Equation in Thin
-Landau Equflion
to ffiethe Ginzburg-Landau$\mathrm{H}\mathrm{i}\mathrm{d}\infty$$\mathrm{D}\mathrm{o}\mathrm{m}\dot{u}\mathrm{n}$$\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{u}\dot{\mathrm{h}}\mathrm{o}\mathrm{n}\mathrm{s}$$\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{u}\dot{\mathrm{h}}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{L}\mathrm{o}$$\mathrm{a}$$\mathrm{G}\mathrm{i}_{\mathrm{o}\mathrm{i}}\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{g}$

森田
aeffl

龍谷大・理工$\not\in’\delta^{\backslash }\text{大・理}\mathrm{I}$Reda)$—————56$$————-$

善久 ((Yos 石.sa Morita)$\mathrm{F}\lambda$$\mathrm{Y}\mathrm{o}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{a}$sysRS ofFree boundaIy problem and its applications to oeaction4iffi1Sion sySRs
7. Foee$———————————————————–63$$——————————————————\cdot$
activator-inhibitor
CyriI B. Muratov
Toch.
New Jersey Inst. of Taeh.
media
media———–79
of ffaveling fionts in spatially
8. Bounds for$\mathfrak{h}’\mathrm{p}\mathrm{e}$$\mathrm{B}.$$\mathrm{p}\varpi \mathrm{i}\mathrm{o}\mathrm{d}\mathrm{i}\mathrm{c}$$\mathrm{e}\mathrm{f}\mathrm{f}\infty \mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{s}\mathrm{p}\infty \mathrm{d}\mathrm{s}$

中村

電通大

健一 (Ken-Ic 石 N 政 mura)

9. Strong Intcracfions among Particlelke Solutions in C .ssipafive Systems
酉浦北大・電子科学研-1-

廉政 (Yasumasa N 可石\mbox{\boldmath $\varpi$}a)88

10. Traveling waves in————————————- 101
mixtures—————————mixtures$\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}- \mathrm{s}\mathrm{e}\mathrm{p}\mathrm{m}\mathrm{f}\dot{\mathrm{i}}\mathrm{n}\mathrm{g}_{\mathrm{I}}\mathrm{e}w\dot{\mathrm{h}}\mathrm{v}\mathrm{e}$$\mathrm{p}\mathrm{h}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{s}\mathrm{e}\mathrm{p}\mathrm{m}\mathrm{f}\dot{\mathrm{i}}\mathrm{n}\mathrm{g}\mathrm{I}\mathrm{e}w\dot{\mathrm{h}}\mathrm{v}\mathrm{e}$広島大・理学/’奥薗透 (Tohru Okuzono)

大田隆夫 (T 處$\mathrm{a}\mathrm{o}$Ohta)

problems from Maxwell-Chem-Simons vortex ffieoly——124
11. Some nonlinear
Univ. Napoli Federico ITonia Ricciardi
equafions by interfaoe equations
12. Approximations of-interior$\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{p}\dot{\mathrm{b}}\mathrm{c}$$\mathrm{d}\mathrm{i}$$\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\dot{\mathrm{h}}\mathrm{o}\mathrm{n}\triangleleft \mathrm{i}\mathrm{f}\mathrm{f}\mathrm{i}_{1}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}$$-\mathrm{b}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{I}\mathrm{y}$$\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}-------- \mathrm{m}-----------------rightarrow---------\cdot-------------- 134$

広島大・理学坂元

国望 (Kuimochi Sakgmo 狛)

13. Singular limit analysis of aggregating pattems in aChemotaxis-Growth model –149
宮崎大・工辻川

亨 (Tohru Tsujikawa)

広島大・理学

昌泰 (Masyasu Mimura)三村

14. Behavior of solutions for asupercritical semilinem heat equation
東北大・理学柳田-2-

英二 (Eiji Yanagida)161