TY - JOUR

T1 - Fractional Diffusion Limit for Collisional Kinetic Equations

AU - Mellet, Antoine

AU - Mischler, Stéphane

AU - Mouhot, Clément

N1 - 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.

PY - 2010/8/20

Y1 - 2010/8/20

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/598362

UR - http://link.springer.com/10.1007/s00205-010-0354-2

UR - http://www.scopus.com/inward/record.url?scp=78751650015&partnerID=8YFLogxK

U2 - 10.1007/s00205-010-0354-2

DO - 10.1007/s00205-010-0354-2

M3 - Article

SN - 0003-9527

VL - 199

SP - 493

EP - 525

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 2

ER -