Fractional Diffusion Limit for Collisional Kinetic Equations

Antoine Mellet, Stéphane Mischler, Clément Mouhot

Research output: Contribution to journalArticlepeer-review

88 Scopus citations

Abstract

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.
Original languageEnglish (US)
Pages (from-to)493-525
Number of pages33
JournalArchive for Rational Mechanics and Analysis
Volume199
Issue number2
DOIs
StatePublished - Aug 20 2010
Externally publishedYes

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