On Rosenau-Type Approximations to Fractional Diffusion Equations
Mathematical Physics
2014-03-14 v1 math.MP
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 L\'evy stable law) at large times.
Cite
@article{arxiv.1403.3182,
title = {On Rosenau-Type Approximations to Fractional Diffusion Equations},
author = {Giulia Furioli and Ada Pulvirenti and Elide Terraneo and Giuseppe Toscani},
journal= {arXiv preprint arXiv:1403.3182},
year = {2014}
}