Fractional Diffusion Limit for Collisional Kinetic Equations

Antoine Mellet, Stéphane Mischler, Clément Mouhot

Research output: Contribution to journalArticlepeer-review

105 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

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: ANTOINE MELLET gratefully thanks the CEREMADE at the Universite Paris Dauphine, where most of this research was performed, for its hospitality. ANTOINE MELLET was also partially supported by NSERC Grant 341253-07. CLEMENT MOUHOT would like to thank Cambridge University who provided repeated hospitality in 2009 and 2010 thanks to the Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST). The authors thank JEAN DOLBEAULT AND STEFANO OLLA for fruitful discussions during the preparation of this work.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

Fingerprint

Dive into the research topics of 'Fractional Diffusion Limit for Collisional Kinetic Equations'. Together they form a unique fingerprint.

Cite this