Fractional Diffusion Limit for Collisional Kinetic Equations

Handle URI:
http://hdl.handle.net/10754/598362
Title:
Fractional Diffusion Limit for Collisional Kinetic Equations
Authors:
Mellet, Antoine; Mischler, Stéphane; Mouhot, Clément
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.
Citation:
Mellet A, Mischler S, Mouhot C (2010) Fractional Diffusion Limit for Collisional Kinetic Equations. Archive for Rational Mechanics and Analysis 199: 493–525. Available: http://dx.doi.org/10.1007/s00205-010-0354-2.
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
20-Aug-2010
DOI:
10.1007/s00205-010-0354-2
Type:
Article
ISSN:
0003-9527; 1432-0673
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorMellet, Antoineen
dc.contributor.authorMischler, Stéphaneen
dc.contributor.authorMouhot, Clémenten
dc.date.accessioned2016-02-25T13:19:24Zen
dc.date.available2016-02-25T13:19:24Zen
dc.date.issued2010-08-20en
dc.identifier.citationMellet A, Mischler S, Mouhot C (2010) Fractional Diffusion Limit for Collisional Kinetic Equations. Archive for Rational Mechanics and Analysis 199: 493–525. Available: http://dx.doi.org/10.1007/s00205-010-0354-2.en
dc.identifier.issn0003-9527en
dc.identifier.issn1432-0673en
dc.identifier.doi10.1007/s00205-010-0354-2en
dc.identifier.urihttp://hdl.handle.net/10754/598362en
dc.description.abstractThis 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.en
dc.description.sponsorshipANTOINE 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.en
dc.publisherSpringer Natureen
dc.titleFractional Diffusion Limit for Collisional Kinetic Equationsen
dc.typeArticleen
dc.identifier.journalArchive for Rational Mechanics and Analysisen
dc.contributor.institutionUniversity of Maryland, College Park, United Statesen
dc.contributor.institutionCentre de Recherche en Mathematiques de la Decision, Paris, Franceen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionEcole Normale Superieure, Paris, Franceen
kaust.grant.numberKUK-I1-007-43en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.