Fractional Diffusion Limit for Collisional Kinetic Equations

By Antoine Mellet, St'ephane Mischler, Clément Mouhot. 2008

200 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1a504bffb375f11fa3108c6d69d58f5511564fcd

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces (2017, background): “Such “restricted” Lévymotions show up an importantmodels in both applied mathematics and applied probability [3, 5, 11, 20, 29, 40, 46], as well as in models in biology and ecology [27, 45].”
Hitchhiker's guide to the fractional Sobolev spaces (2011, unknown): “[64] A.”
Central limit theorems for additive functionals of ergodic Markov diffusions processes (2011, background): “More generally, we believe that a whole category of diffusion limits which appear in the asymptotic analysis of evolution partial differential equations of Fokker-Planck type enters indeed the framework of the central limit theorems we shall discuss.”