Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2011

Fractional diffusion limit for collisional kinetic equations

Résumé

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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Dates et versions

hal-00321478 , version 1 (15-09-2008)
hal-00321478 , version 2 (30-09-2008)

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Antoine Mellet, Stéphane Mischler, Clément Mouhot. Fractional diffusion limit for collisional kinetic equations. Archive for Rational Mechanics and Analysis, 2011, 199 (2), pp.493-525. ⟨10.1007/s00205-010-0354-2⟩. ⟨hal-00321478v2⟩
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