Communications in Mathematical Sciences

Volume 13 (2015)

Number 5

On Rosenau-type approximations to fractional diffusion equations

Pages: 1163 – 1191

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n5.a5

Authors

Giulia Furioli (University of Bergamo, Dalmine, Italy)

Ada Pulvirenti (Department of Mathematics, University of Pavia, Italy)

Elide Terraneo (Department of Mathematics, University of Milan, Italy)

Giuseppe Toscani (Department of Mathematics, University of Pavia, Italy)

Abstract

Owing to the Rosenau argument [P. Rosenau, Physical Review A, 46, 12–15, 1992], 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.

Keywords

fractional diffusion equations, non-local models, Fourier metrics, Rosenau approximation, Lévy-type distributions

2010 Mathematics Subject Classification

35B40, 35K55, 35K60, 35K65

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