Communications in Mathematical Sciences
Volume 13 (2015)
On Rosenau-type approximations to fractional diffusion equations
Pages: 1163 – 1191
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.
fractional diffusion equations, non-local models, Fourier metrics, Rosenau approximation, Lévy-type distributions
2010 Mathematics Subject Classification
35B40, 35K55, 35K60, 35K65