Nonlinear diffusions as limit of kinetic equations with relaxation collision kernels
Date
2007Link to item file
http://hal.archives-ouvertes.fr/hal-00005892/en/Dewey
AnalyseSujet
Kinetic equation; Macroscopic limit; Diffusion limit; Boltzmann equation; Equilibrium distribution function; Gibbs state; Porous medium equation; Fast diffusion equation; Relaxation time approximation; Compensated compactnessJournal issue
Archive for Rational Mechanics and AnalysisVolume
186Number
1Publication date
2007Article pages
133-158Publisher
SpringerCollections
Metadata
Show full item recordAuthor
Dolbeault, Jean
Markowich, Peter
Oelz, Dietmar
Schmeiser, Christian
Type
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
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