, Volume 199, Issue 2, pp 493-525
Date: 20 Aug 2010

Fractional Diffusion Limit for Collisional Kinetic Equations

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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.

Communicated by P.-L. Lions