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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 solutions in an appropriate domain of attraction of the equilibrium distribution converge to solutions of a Fokker-Planck equation with a fractional diffusion operator.

preprint2011arXivOpen access
G. FurioliA. PulvirentiE. TerraneoG. Toscani
math.AP
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Open access4 authors1 topic
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G. FurioliA. PulvirentiE. TerraneoG. Toscani

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