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arXiv · 1403.3182

On Rosenau-Type Approximations to Fractional Diffusion Equations

Giulia Furioli·Ada Pulvirenti·Elide Terraneo·Giuseppe Toscani
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Abstract

Owing to the Rosenau argument in Physical Review A, 46 (1992), pag. 12-15, 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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Giulia Furioli, Ada Pulvirenti, Elide Terraneo, Giuseppe Toscani. 2014-03-13. On Rosenau-Type Approximations to Fractional Diffusion Equations. https://arxiv.org/abs/1403.3182

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