Boundary conditions for fractional diffusion (Reprinted from Journal of Computational and Applied Mathematics, vol 336, pg 408-424, 2018)

被引：0
|
作者：
Baeumer, Boris [1 ]
Kovacs, Mihaly [2 ,3 ]
Meerschaert, Mark M. [4 ]
Sankaranarayanan, Harish [5 ]
机构：
[1] Univ Otago, Dunedin, New Zealand
[2] Chalmers Univ Technol, Gothenburg, Sweden
[3] Univ Gothenburg, Gothenburg, Sweden
[4] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA
[5] Michigan State Univ, E Lansing, MI 48824 USA
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 339卷
基金：
美国国家科学基金会;
关键词：
Fractional calculus; Boundary value problem; Numerical solution; Well-posed; PARTIAL-DIFFERENTIAL-EQUATIONS; ANOMALOUS DIFFUSION; NUMERICAL-SOLUTION; VECTOR CALCULUS; DISPERSION; APPROXIMATIONS; MODELS; LAW; DERIVATIVES; TRANSPORT;
D O I：
10.1016/j.cam.2018.03.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2018 Published by Elsevier B.V.
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页码：414 / 430
页数：17
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