Journal ArticleDOI
Quasilinear elliptic-parabolic differential equations
TLDR
In this article, the authors considered the special cases of an elliptic equation with time as parameter, that is, b(z)= 0, and the standard parabolic equation, that are, b (z)=z are included.Abstract:
The structure conditions are the ellipticity of a and the (weak) monotonicity of b, and b has to be a subgradient in case m > 1. First we treat the case that b is continuous, and later (Sect. 4) we include Stefan problems, that is, we allow b to have jumps. The special cases of an elliptic equation with time as parameter, that is, b(z)= 0, and the standard parabolic equation, that is, b(z)=z are included. Some special single equations of mixed elliptic and parabolic type are given in the following. The gas flow through a porous medium is described by the equationread more
Citations
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Journal ArticleDOI
The geometry of dissipative evolution equations: the porous medium equation
TL;DR: In this paper, the authors show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural, and they use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.
Journal ArticleDOI
Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
TL;DR: In this article, the existence and uniqueness of generalized solutions of the Cauchy problem and of initial boundary-value problems are discussed and the character of the dependence on the data is discussed.
Journal ArticleDOI
Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media
TL;DR: In this article, an algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions.
Journal ArticleDOI
Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
TL;DR: In this paper, the authors analyzed the large-time asymptotics of quasilinear (possibly) degenerate parabolic systems in three cases: 1) scalar problems with confinement by a uniformly convex potential, 2) unconfined scalar equations and 3) un-confined systems.
L1-Contraction and uniqueness for quasilinear ellipitic-parabolic equations
TL;DR: In this article, the authors demontrons le principe de contraction en norme L 1 and lunicite des solutions for les equations quasilineaires du type elliptique-parabolique.
References
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Book
Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
TL;DR: In this article, Operateurs Maximaux Monotones: Et Semi-Groupes De Contractions Dans Les Espaces De Hllbert are described and discussed. But the focus is not on the performance of the operators.
Journal Article
A semilinear equation in $L^1 (\mathbb {R}^N)$
Book ChapterDOI
An Introduction to Evolution Governed by Accretive Operators
TL;DR: In this article, a broad range of interesting problems in partial differential equations arising from physical models have been discussed, including the evolution problems, which describe the change of a physical system in time, or result from seeking stationary solutions of some evolution problem.