Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 44, Issue 2, Pages 827-850Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110836572
Keywords
dissipative kinetic models; Levy-type distributions; fractional diffusion equations
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- MIUR
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This paper is devoted to the grazing collision limit of the inelastic Kac model introduced in [A. Pulvirenti and G. Toscani, J. Statist. Phys., 14 (2004), pp. 1453-1480], when the equilibrium distribution function is a heavy-tailed Levy-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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