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.
On Rosenau-type approximations to fractional diffusion equations / G. Furioli, A. Pulvirenti, E. Terraneo, G. Toscani. - In: COMMUNICATIONS IN MATHEMATICAL SCIENCES. - ISSN 1539-6746. - 13:5(2015), pp. 1163-1191. [10.4310/CMS.2015.v13.n5.a5]
On Rosenau-type approximations to fractional diffusion equations.
E. TerraneoPenultimo
;
2015
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.
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