This paper is devoted to the grazing collision limit of the inelastic Kac model, 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 research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.
The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium
PULVIRENTI, ADA;TOSCANI, GIUSEPPE
2012-01-01
Abstract
This paper is devoted to the grazing collision limit of the inelastic Kac model, 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 research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.File in questo prodotto:
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