pinecone/core-2020-05-10-deduplication huggingface dataset:
Seasonal and inter-annual variations in carbon fluxes in a tropical river system (Tana River, Kenya)

The hydrological status of river systems is expected to change due to dam operations and climate change. This will affect the riverine fluxes of sediment and carbon (C). In rivers with strong seasonal and inter-annual variability, quantification and extrapolation of sediment and C fluxes can be a challenge as measurement periods are often too short to cover all hydrological conditions. We studied the dynamics of the Tana River (Kenya) from 2012 to 2014 through daily monitoring of sediment concentrations at three sites (Garissa, Tana River Primate Reserve and Garsen) and daily monitoring of C concentrations in Garissa and Garsen during three distinct seasons. A bootstrap method was applied to calculate the range of sediment and C fluxes as a function of annual discharge by using daily discharge data (1942–2014). Overall, we estimated that on average, sediment and carbon were retained in this 600 km long river section between Garissa to Garsen over the 73 years (i.e., fluxes were higher at the upstream site than downstream): integration over all simulations resulted in an average net retention of sediment (~ 2.9 Mt year− 1), POC (~ 18,000 tC year− 1), DOC (~ 920 tC year− 1) and DIC (~ 1200 tC year− 1). To assess the impact of hydrological variations, we constructed four different hydrological scenarios over the same period. Although there was significant non-linearity and difference between the C species, our estimates generally predicted a net increase of C retention between the upstream and downstream site when the annual discharge would decrease, for example caused by an increase of irrigation with reservoir water. When simulating an increase in the annual discharge, e.g. as a potential effect of climate change, we predicted a decrease in C retention.Peer reviewe
Weighted norm inequalities, off-diagonal estimates and elliptic
  operators. Part II: Off-diagonal estimates on spaces of homogeneous type

This is the second part of a series of four articles on weighted norm
inequalities, off-diagonal estimates and elliptic operators. We consider a
substitute to the notion of pointwise bounds for kernels of operators which
usually is a measure of decay. This substitute is that of off-diagonal
estimates expressed in terms of local and scale invariant $L^p-L^q$ estimates.
We propose a definition in spaces of homogeneous type that is stable under
composition. It is particularly well suited to semigroups. We study the case of
semigroups generated by elliptic operators.Comment: 40 pages. Second of 4 papers. Can be read independentl
Analyticity and Riesz basis property of semigroups associated to damped
  vibrations

Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract
Hilbert space are considered. Such equations are often used as a model for
transverse motions of thin beams in the presence of damping. We derive various
properties of the operator matrix $A$ associated with the second order problem
above. We develop sufficient conditions for analyticity of the associated
semigroup and for the existence of a Riesz basis consisting of eigenvectors and
associated vectors of $A$ in the phase space
Asymptotics and analytic modes for the wave equation in similarity
  coordinates

We consider the radial wave equation in similarity coordinates within the
semigroup formalism. It is known that the generator of the semigroup exhibits a
continuum of eigenvalues and embedded in this continuum there exists a discrete
set of eigenvalues with analytic eigenfunctions. Our results show that, for
sufficiently regular data, the long time behaviour of the solution is governed
by the analytic eigenfunctions. The same techniques are applied to the linear
stability problem for the fundamental self--similar solution $\chi_T$ of the
wave equation with a focusing power nonlinearity. Analogous to the free wave
equation, we show that the long time behaviour (in similarity coordinates) of
linear perturbations around $\chi_T$ is governed by analytic mode solutions. In
particular, this yields a rigorous proof for the linear stability of $\chi_T$
with the sharp decay rate for the perturbations.Comment: This new version fixes a problem with an incorrect use of spectral
  projections; results remain unchange
Diffuse measures and nonlinear parabolic \ud
equations

Given a parabolic cylinder $Q =(0,T)\times\Omega$, where $\Omega\subset \rn$ is a bounded domain, we \ud
prove new properties of solutions of \ud
\[\ud
u_t-\Delta_p u = \mu \quad \text{in $Q$}\ud
\]\ud
with Dirichlet boundary conditions, where $\mu$ is a finite Radon measure in $Q$. We first prove  a priori estimates on the $p$-parabolic capacity of level sets of $u$. We then show that diffuse measures (i.e.\@ measures which do not charge sets of zero parabolic $p$-capacity) can be strongly approximated by the measures  $\mu_k = (T_k(u))_t-\Delta_p(T_k(u))$, and  we introduce a new notion of renormalized solution based on this property. We finally apply our new approach  to prove the existence of solutions of \ud
$$\ud
u_t-\Delta_{p} u + h(u)=\mu \quad \text{in $Q$,}\ud
$$\ud
for any function $h$ such that  $h(s)s\geq 0$ and for any diffuse measure $\mu$; when $h$ is nondecreasing we also prove uniqueness in the renormalized formulation
Well-posedness and asymptotic behavior of a multidimensional model of
  morphogen transport

Morphogen transport is a biological process, occurring in the tissue of
living organisms, which is a determining step in cell differentiation. We
present rigorous analysis of a simple model of this process, which is a system
coupling parabolic PDE with ODE. We prove existence and uniqueness of solutions
for both stationary and evolution problems. Moreover we show that the solution
converges exponentially to the equilibrium in $C^1\times C^0$ topology. We
prove all results for arbitrary dimension of the domain. Our results improve
significantly previously known results for the same model in the case of one
dimensional domain
A mixed problem of linear elastodynamics

This paper is devoted to a semigroup approach to an initial-boundary value problem of linear elastodynamics in the case where the boundary condition is a regularization of the genuine mixed displacement-traction boundary condition. More precisely, it is a smooth linear combination of displacement and traction boundary conditions, but is not equal to the pure traction boundary condition. Some previous results with mixed displacement-traction boundary condition are due to Inoue and Ito. The crucial point in our semigroup approach is to generalize the classical variational approach to the degenerate case, by using the theory of fractional powers of analytic semigroups
The regular part of second-order differential sectorial forms with
  lower-order terms

We present a formula for the regular part of a sectorial form that represents
a general linear second-order differential expression that may include
lower-order terms. The formula is given in terms of the original coefficients.
It shows that the regular part is again a differential sectorial form and
allows to characterise when also the singular part is sectorial. While this
generalises earlier results on pure second-order differential expressions, it
also shows that lower-order terms truly introduce new behaviour.Comment: 11 page
Cosine families and semigroups really differ

We reveal three surprising properties of cosine families, distinguishing them from semigroups of operators: (1) A single trajectory of a cosine family is either strongly continuous or not measurable. (2) Pointwise convergence of a sequence of equibounded cosine families implies that the convergence is almost uniform for time in the entire real line; in particular, cosine families cannot be perturbed in a singular way. (3) A non-constant trajectory of a bounded cosine family does not have a limit at infinity; in particular, the rich theory of asymptotic behaviour of semigroups does not have a counterpart for cosine families. In addition, we show that equibounded cosine families that converge strongly and almost uniformly in time may fail to converge uniformly.Adam Bobrowski and Wojciech Chojnack
Some results on the large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations

International audienceSystems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. The large time behavior for systems of Hamilton-Jacobi equations have been obtained by Camilli-Loreti-Ley and the author (2012) and Mitake-Tran (2012) under quite strict conditions. In this work, we use a PDE approach to extend the convergence result proved by Barles-Souganidis (2000) in the scalar case. This general result permits us to treat lot of general cases, for instance, systems with nonconvex Hamiltonians and systems with strictly convex Hamiltonians. We also obtain some other convergence results under different assumptions, these results give a clearer view on the large time behavior for systems of Hamilton-Jacobi equations
Phase-lag heat conduction: decay rates for limit problems and well-posedness

The final publication is available at Springer via http://dx.doi.org/10.1007/s00028-014-0242-6.In two recent papers, the authors have studied conditions on the relaxation parameters in order to guarantee the stability or instability of solutions for the Taylor approximations to dual-phase-lag and three-phase-lag heat conduction equations. However, for several limit cases relating to the parameters, the kind of stability was unclear. Here, we analyze these limit cases and clarify whether we can expect exponential or slow decay for the solutions. Moreover, rather general well-posedness results for three-phase-lag models are presented. Finally, the exponential stability expected by spectral analysis is rigorously proved exemplarily.Peer ReviewedPostprint (author’s final draft
Polynomial Stability of Semigroups Generated by Operator Matrices

In this paper we study the stability properties of strongly continuous
semigroups generated by block operator matrices. We consider triangular and
full operator matrices whose diagonal operator blocks generate polynomially
stable semigroups. As our main results, we present conditions under which also
the semigroup generated by the operator matrix is polynomially stable. The
theoretic results are applied to deriving conditions for the polynomial
stability of a system consisting of a two-dimensional and a one-dimensional
damped wave equations.Comment: 28 pages, 1 figures, submitte
Exponentially weighted resolvent estimates for complex
  Ornstein-Uhlenbeck systems

In this paper we study differential operators of the form \begin{align*}
\left[\mathcal{L}_\infty v \right](x) = A\triangle v(x) + \left\langle
Sx,\nabla v(x) \right\rangle - Bv(x), \,x \in \mathbb{R}^d, \,d \geqslant 2,
\end{align*} for matrices $A,B\in\mathbb{C}^{N,N}$, where the eigenvalues of
$A$ have positive real parts. The sum $A\triangle v(x) + \left\langle Sx,
\nabla v(x) \right\rangle$ is known as the Ornstein-Uhlenbeck operator with an
unbounded drift term defined by a skew-symmetric matrix $S\in\mathbb{R}^{d,d}$.
Differential operators such as $\mathcal{L}_{\infty}$ arise as linearizations
at rotating waves in time-dependent reaction diffusion systems. The results of
this paper serve as foundation for proving exponential decay of such waves.
Under the assumption that $A$ and $B$ can be diagonalized simultaneously we
construct a heat kernel matrix $H(x,\xi,t)$ of $\mathcal{L}_{\infty}$ that
solves the evolution equation $v_t=\mathcal{L}_{\infty}v$. In the following we
study the Ornstein-Uhlenbeck semigroup \begin{align*} \left[ T(t)v\right](x) =
\int_{\mathbb{R}^d} H(x,\xi,t) v(\xi) d\xi,\,x \in \mathbb{R}^d,\, t>0,
\end{align*} in exponentially weighted function spaces. This is used to derive
resolvent estimates for $\mathcal{L}_{\infty}$ in exponentially weighted
$L^p$-spaces $L^p_{\theta} (\mathbb{R}^d,\mathbb{C}^N)$, $1\leqslant p<\infty$,
as well as in exponentially weighted $C_{\mathrm{b}}$-spaces
$C_{\mathrm{b},\theta}(\mathbb{R}^d,\mathbb{C}^N)$.Comment: 35 pages, J. Evol. Equ. (published online 2015
Nonlinear Maximal Monotone Extensions of Symmetric Operators

Given a linear semi-bounded symmetric operator $S\ge -\omega$, we explicitly
define, and provide their nonlinear resolvents, nonlinear maximal monotone
operators $A_\Theta$ of type $\lambda>\omega$ (i.e. generators of one-parameter
continuous nonlinear semi-groups of contractions of type $\lambda$) which
coincide with the Friedrichs extension of $S$ on a convex set containing
${\mathscr D}(S)$. The extension parameter $\Theta\subset{\mathfrak
h}\times{\mathfrak h}$ ranges over the set of nonlinear maximal monotone
relations on an auxiliary Hilbert space $\mathfrak h$ isomorphic to the
deficiency subspace of $S$. Moreover $A_\Theta+\lambda$ is a sub-potential
operator (i.e. is the sub-differential of a lower semicontinuos convex
function) whenever $\Theta$ is sub-potential. Examples describing Laplacians
with nonlinear singular perturbations supported on null sets and Laplacians
with nonlinear boundary conditions on a bounded set are given.Comment: Revised final version. To appear in Journal of Evolution Equation
Properties of the solutions of delocalised coagulation and inception
  problems with outflow boundaries

Well posedness is established for a family of equations modelling particle
populations undergoing delocalised coagulation, advection, inflow and outflow
in a externally specified velocity field. Very general particle types are
allowed while the spatial domain is a bounded region of $d$-dimensional space
for which every point lies on exactly one streamline associated with the
velocity field. The problem is formulated as a semi-linear ODE in the Banach
space of bounded measures on particle position and type space. A local
Lipschitz property is established in total variation norm for the propagators
(generalised semi-groups) associated with the problem and used to construct a
Picard iteration that establishes local existence and global uniqueness for any
initial condition. The unique weak solution is shown further to be a
differentiable or at least bounded variation strong solution under smoothness
assumptions on the parameters of the coagulation interaction. In the case of
one spatial dimension strong differentiability is established even for
coagulation parameters with a particular bounded variation structure in space.
This one dimensional extension establishes the convergence of the simulation
processes studied in [Patterson, Stoch. Anal. Appl. 31, 2013] to a unique and
differentiable limit
Optimal energy decay in a one-dimensional coupled wave-heat system

We study a simple one-dimensional coupled wave-heat system and obtain a sharp
estimate for the rate of energy decay of classical solutions. Our approach is
based on the asymptotic theory of $C_0$-semigroups and in particular on a
result due to Borichev and Tomilov (Math. Ann., 2010), which reduces the
problem of estimating the rate of energy decay to finding a growth bound for
the resolvent of the semigroup generator. This technique not only leads to an
optimal result, it is also simpler than the methods used by other authors in
similar situations.Comment: To appear in Journal of Evolution Equation
How to estimate observability constants of one-dimensional wave equations? Propagation versus spectral methods

For a given bounded connected domain in $\R^n$ , the issue of computing the observability constant associated to a wave operator, an observation time $T$ and a generic observation subdomain constitutes in general a hard task, even for one-dimensional problems. In this work, we introduce and describe two methods to provide precise (and even sharp in some cases) estimates of observability constants for general one dimensional wave equations: the first one uses a spectral decomposition of the solution of the wave equation whereas the second one is based on a propagation argument along the characteristics. Both methods are extensively described and we then comment on the advantages and drawbacks of each one. The discussion is illustrated by several examples and numerical simulations. As a byproduct, we deduce from the main results estimates of the cost of control (resp. the decay rate of the energy) for several controlled (resp. damped) wave equations
On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators

The paper contains a representation formula for positive solutions of linear degenerate second-order equations of the form of "sum of squares of vector fields plus a drift term" where the vector fields X_j's satisfy the Hörmander condition. It is assumed that X_j's are invariant under left translations of a Lie group and the corresponding paths satisfy a local admissibility criterion. The representation formula is established by an analytic approach based on Choquet theory. As a consequence we obtain Liouville-type theorems and uniqueness results for the positive Cauchy problem
Pointwise weak existence for diffusions associated with degenerate
  elliptic forms and 2-admissible weights

Using analysis for 2-admissible functions in weighted Sobolev spaces and
stochastic calculus for possibly degenerate symmetric elliptic forms, we
construct weak solutions to a wide class of stochastic differential equations
starting from an explicitly specified subset in Euclidean space. The solutions
have typically unbounded and discontinuous drift but may still in some cases
start from all points of $\mathbb{R}^d$ and thus in particular from those where
the drift terms are infinite. As a consequence of our approach we are able to
provide new non-explosion criteria for the unique strong solutions of
\cite{Zh}.Comment: Minor corrections, modified title, reference [19] update
Cauchy Problems for Parabolic Equations in Sobolev-Slobodeckii and
  H\"older Spaces on Uniformly Regular Riemannian Manifolds

In this paper we establish optimal solvability results, that is, maximal
regularity theorems, for the Cauchy problem for linear parabolic differential
equations of arbitrary order acting on sections of tensor bundles over
boundaryless complete Riemannian manifolds with bounded geometry. We employ an
anisotropic extension of the Fourier multiplier theorem for arbitrary Besov
spaces introduced in earlier by the author. This allows for a unified treatment
of Sobolev-Slobodeckii and little H\"older spaces. In the flat case we recover
classical results for Petrowskii-parabolic Cauchy problems.Comment: typos have been corrected and additional references have been
  include
Mathematical Analysis of a Clonal Evolution Model of Tumour Cell
  Proliferation

We investigate a partial differential equation model of a cancer cell
population, which is structured with respect to age and telomere length of
cells. We assume a continuous telomere length structure, which is applicable to
the clonal evolution model of cancer cell growth. This model has a non-standard
non-local boundary condition. We establish global existence of solutions and
study their qualitative behaviour. We study the effect of telomere restoration
on cancer cell dynamics. Our results indicate that without telomere
restoration, the cell population extinguishes. With telomere restoration,
exponential growth occurs in the linear model. We further characterise the
specific growth behaviour of the cell population for special cases. We also
study the effects of crowding induced mortality on the qualitative behaviour,
and the existence and stability of steady states of a nonlinear model
incorporating crowding effect. We present examples and extensive numerical
simulations, which illustrate the rich dynamic behaviour of the linear and
nonlinear models.Comment: 36 pages, 12 figure
Positive and negative results on the internal controllability of parabolic equations coupled by zero and first order terms

International audienceThis paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain Ω of R^N  with coupling terms of zero and first orders and one control localized in some arbitrary nonempty open subset ω of the domain Ω. We prove the null controllability under a new sufficient condition and we also provide the first example of a not approximately controllable system in the case where the support of one of the nontrivial first order coupling terms intersects the control domain ω
Construction of a surface integral under local Malliavin assumption and
  integration by parts formulae

In this paper, we consider convex sets $K_r = \{g \ge r\}$ in an infinite
dimensional Hilbert space, where $g$ is suitably related to a reference
Gaussian measure $\mu$ in $H$. We first show how to define a surface measure on
the level sets $\{g = r\}$ that is related to $\mu$. This allows to introduce
an integration-by-parts formula in $H$. This formula can be applied in several
important constructions, as for instance the case where $\mu$ is the law of a
(Gaussian) stochastic process and $H$ is the space of its trajectoriesComment: 22 page
Classical well-posedness in dispersive equations with nonlinearities of
  mild regularity, and a composition theorem in Besov spaces

For both localized and periodic initial data, we prove local existence in
classical energy space $H^s, s>\frac{3}{2}$, for a class of dispersive
equations $u_{t}+(n(u))_{x}+Lu_{x}=0$ with nonlinearities of mild regularity.
Our results are valid for symmetric Fourier multiplier operators $L$ whose
symbol is of temperate growth, and $n(\cdot)$ in local Sobolev space
$H^{s+2}_{\mathrm{loc}}(\mathbb{R})$. In particular, the results include
non-smooth and exponentially growing nonlinearities. Our proof is based on a
combination of semi-group methods and a new composition result for Besov
spaces. In particular, we extend a previous result for Nemytskii operators on
Besov spaces on $\mathbb{R}$ to the periodic setting by using the
difference-derivative characterization of Besov spaces
Sharp growth rates for semigroups using resolvent bounds

We study growth rates for strongly continuous semigroups. We prove that a
growth rate for the resolvent on imaginary lines implies a corresponding growth
rate for the semigroup if either the underlying space is a Hilbert space, or
the semigroup is asymptotically analytic, or if the semigroup is positive and
the underlying space is an $L^{p}$-space or a space of continuous functions. We
also prove variations of the main results on fractional domains; these are
valid on more general Banach spaces. In the second part of the article we apply
our main theorem to prove optimality in a classical example by Renardy of a
perturbed wave equation which exhibits unusual spectral behavior.Comment: 20 pages. To appear in Journal of Evolution Equation