Fractional diffusion limit for collisional kinetic equations
Accepted version
Peer-reviewed
Repository URI
Repository DOI
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