Boundary conditions for fractional diffusion
Artikel i vetenskaplig tidskrift, 2018

This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involve fractional derivatives. The Caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion, since the resulting boundary value problem is not positivity preserving.

Well-posed

Fractional calculus

Numerical solution

Boundary value problem

Författare

Boris Baeumer

University of Otago

Mihaly Kovacs

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Mark M. Meerschaert

Michigan State University

Harish Sankaranarayanan

Michigan State University

Journal of Computational and Applied Mathematics

0377-0427 (ISSN)

Vol. 336 408-424

Ämneskategorier

Teknisk mekanik

Beräkningsmatematik

Matematisk analys

DOI

10.1016/j.cam.2017.12.053