The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium

Details The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium

2011-05-25

arxiv.org/abs/1105.5045v1

Mathematics

Analysis of PDEs

27 pages

Scientific paper

This paper is devoted to the grazing collision limit of the inelastic Kac model introduced in [A. Pulvirenti and G. Toscani. J. Statist. Phys., 114(5-6):1453--1480, 2004], when the equilibrium distribution function is a heavy-tailed L\'evy-type distribution with infinite variance. We prove that solutions in an appropriate domain of attraction of the equilibrium distribution converge to solutions of a Fokker-Planck equation with a fractional diffusion operator.

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