Fractional diffusion limit for collisional kinetic equations: A moments method
Analysis of PDEs
2009-10-09 v1
Abstract
This paper is devoted to hydrodynamic limits of linear kinetic equations when the thermodynamical equilibrium is described by a heavy-tail distribution function rather than a Maxwellian distribution. We show that the long time/small mean free path behavior of the solution of the kinetic equation is described by a fractional diffusion equation. The method that we introduce is somewhat reminiscent of the so-called "moments method" which plays an important role in kinetic theory.
Cite
@article{arxiv.0910.1570,
title = {Fractional diffusion limit for collisional kinetic equations: A moments method},
author = {Antoine Mellet},
journal= {arXiv preprint arXiv:0910.1570},
year = {2009}
}