Boundary conditions for fractional diffusion
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Publication:1696458
DOI10.1016/J.CAM.2017.12.053zbMATH Open1386.35424arXiv1706.07991OpenAlexW2727609060WikidataQ60580250 ScholiaQ60580250MaRDI QIDQ1696458
Author name not available (Why is that?)
Publication date: 14 February 2018
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1706.07991
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