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 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.
The Grazing Collision Limit of the Inelastic Kac Model around a Lévy-type Equilibrium / G. Furioli, A. Pulvirenti, E. Terraneo, G. Toscani. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 44:2(2012), pp. 827-850.
The Grazing Collision Limit of the Inelastic Kac Model around a Lévy-type Equilibrium
E. TerraneoPenultimo
;
2012
Abstract
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 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.
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