Owing to Rosenau argument [28], originally proposed to obtain a regularized version of the Chapman-Enskog expansion of hydrodynamics, we introduce a non-local linear kinetic equation which approximates a fractional diffusion equation. We then show that the solution to this approximation, apart of a rapidly vanishing in time perturbation, approaches the fundamental solution of the fractional diffusion (a Lévy stable law) at large times.

On Rosenau-type approximation to fractional diffusion equations

FURIOLI, Giulia Maria Dalia;
2014

Abstract

Owing to Rosenau argument [28], originally proposed to obtain a regularized version of the Chapman-Enskog expansion of hydrodynamics, we introduce a non-local linear kinetic equation which approximates a fractional diffusion equation. We then show that the solution to this approximation, apart of a rapidly vanishing in time perturbation, approaches the fundamental solution of the fractional diffusion (a Lévy stable law) at large times.
Furioli, Giulia Maria Dalia; Pulvirenti, Ada; Terraneo, Elide; Toscani, Giuseppe
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/30859
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