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

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 Lévy-type distribution with infinite variance. We prove that soluti...

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Bibliographic Details
Published in:arXiv.org 2011-05
Main Authors: Furioli, G, Pulvirenti, A, Terraneo, E, Toscani, G
Format: Article
Language:English
Subjects:
Distribution functions
Equilibrium
Fokker-Planck equation
Grazing
Online Access:Get full text
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Summary: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 Lévy-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.
ISSN:2331-8422