Boundary Conditions for Fractional Diffusion
Analysis of PDEs
2017-06-27 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1706.07991,
title = {Boundary Conditions for Fractional Diffusion},
author = {Boris Baeumer and Mihály Kovács and Mark M. Meerschaert and Harish Sankaranarayanan},
journal= {arXiv preprint arXiv:1706.07991},
year = {2017}
}