• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Nonlinear diffusions as limit of kinetic equations with relaxation collision kernels

Thumbnail
Date
2007
Link to item file
http://hal.archives-ouvertes.fr/hal-00005892/en/
Dewey
Analyse
Sujet
Kinetic equation; Macroscopic limit; Diffusion limit; Boltzmann equation; Equilibrium distribution function; Gibbs state; Porous medium equation; Fast diffusion equation; Relaxation time approximation; Compensated compactness
Journal issue
Archive for Rational Mechanics and Analysis
Volume
186
Number
1
Publication date
2007
Article pages
133-158
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00205-007-0049-5
URI
https://basepub.dauphine.fr/handle/123456789/575
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Dolbeault, Jean
Markowich, Peter
Oelz, Dietmar
Schmeiser, Christian
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

Related items

Showing items related by title, author, creator and subject.

  • Structures contrôlées pour les équations aux dérivées partielles 

    Furlan, Marco (2018-06-26) Thèse
  • Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (Large time behavior and steady states) 

    Dolbeault, Jean (1999) Article accepté pour publication ou publié
  • Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation 

    Lafleche, Laurent (2018) Document de travail / Working paper

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.