Date
2007
Lien vers un document non conservé dans cette base
http://hal.archives-ouvertes.fr/hal-00005892/en/
Indexation documentaire
Analyse
Subject
Kinetic equation; Macroscopic limit; Diffusion limit; Boltzmann equation; Equilibrium distribution function; Gibbs state; Porous medium equation; Fast diffusion equation; Relaxation time approximation; Compensated compactness
Nom de la revue
Archive for Rational Mechanics and Analysis
Volume
186
Numéro
1
Date de publication
2007
Pages article
133-158
Nom de l'éditeur
Springer
Auteur
Dolbeault, Jean
Markowich, Peter
Oelz, Dietmar
Schmeiser, Christian
Type
Article accepté pour publication ou publié
Résumé en anglais
Kinetic transport equations with a given confining potential and non-linear relaxation type collision operators are considered. General (monotone) energy dependent equilibrium distributions are allowed with a chemical potential ensuring mass conservation. Existence and uniqueness of solutions is proven for initial data bounded by equilibrium distributions. The diffusive macroscopic limit is carried out using compensated compactness theory. The result are drift-diffusion equations with nonlinear diffusion. The most notable examples are of porous medium or fast diffusion type, with exponent ranging from 0 to 5/3, in dimension 3.
