Fractional Diffusion Limit for Collisional Kinetic Equations
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- Mellet, A., Mischler, S. & Mouhot, C. Arch Rational Mech Anal (2011) 199: 493. doi:10.1007/s00205-010-0354-2
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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.