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Fractional diffusion limit for collisional kinetic equations

Mellet, Antoine; Mischler, Stéphane; Mouhot, Clément (2011), Fractional diffusion limit for collisional kinetic equations, Archive for Rational Mechanics and Analysis, 199, 2, p. 493-525. http://dx.doi.org/10.1007/s00205-010-0354-2

Type
Article accepté pour publication ou publié
Date
2011
Journal name
Archive for Rational Mechanics and Analysis
Volume
199
Number
2
Publisher
Springer
Pages
493-525
Publication identifier
Metadata
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Author(s)
Mellet, Antoine

Mischler, Stéphane

Mouhot, Clément
Abstract (EN)
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.
Subjects / Keywords
diffusion limit; anomalous diffusion limit; mathematical derivation; anomalous heat transport; linear BGK equation; relaxation equation; anomalous diffusive time scale; linear Boltzmann equation; fractional heat equation; fractional diffusion