Repository logo
 

Fractional diffusion limit for collisional kinetic equations

Accepted version
Peer-reviewed

Type

Article

Change log

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 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.

Description

Keywords

math.AP, math.AP, 76P05, 26A33

Journal Title

Archive for Rational Mechanics and Analysis

Conference Name

Journal ISSN

0003-9527

Volume Title

199

Publisher

Springer Nature