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 publiéDate
2011Journal name
Archive for Rational Mechanics and AnalysisVolume
199Number
2Publisher
Springer
Pages
493-525
Publication identifier
Metadata
Show full item recordAbstract (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 diffusionRelated items
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