Fractional Diffusion Limit for Collisional Kinetic Equations

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 situati...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2011-02, Vol.199 (2), p.493-525
Main Authors: Mellet, Antoine, Mischler, Stéphane, Mouhot, Clément
Format: Article
Language:English
Subjects:
Analysis of PDEs
Classical Mechanics
Classical statistical mechanics
Complex Systems
Exact sciences and technology
Fluid- and Aerodynamics
Kinetic theory
Mathematical and Computational Physics
Mathematics
Physics
Physics and Astronomy
Statistical physics, thermodynamics, and nonlinear dynamical systems
Theoretical
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Summary: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-010-0354-2