Fractional diffusion limit for collisional kinetic equations

Details Fractional diffusion limit for collisional kinetic equations Fractional diffusion limit for collisional kinetic equations

2008-09-15

arxiv.org/abs/0809.2455v2

Archive for Rational Mechanics and Analysis (2010) To appear

Mathematics

Analysis of PDEs

Scientific paper

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.

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