Non linear diffusions as limit of kinetic equations with relaxation collision kernels

Jean Dolbeault*, Peter Markowich, Dietmar Oelz, Christian Schmeiser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

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 proved for initial data bounded by equilibrium distributions. The diffusive macroscopic limit is carried out using compensated compactness theory. The results are drift-diffusion equations with non linear diffusion. The most notable examples are of the form ranging from porous medium equations to fast diffusion, with the exponent satisfying 0 < m < 5/3 in R3.

Original languageEnglish (US)
Pages (from-to)133-158
Number of pages26
JournalArchive for Rational Mechanics and Analysis
Volume186
Issue number1
DOIs
StatePublished - Oct 2007

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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