On the time fractional heat equation with obstacle

被引：1

作者：

Alberini, C. ^{[1
]}

Capitanelli, R. ^{[1
]}

D'Ovidio, M. ^{[1
]}

Vita, S. Finzi ^{[2
]}

机构：

[1] Sapienza Univ Roma, Dipartimento SBAI, Rome, Italy

[2] Sapienza Univ Roma, Dipartimento Matemat, Rome, Italy

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 415卷

关键词：

Degenerate parabolic problems; Finite difference methods; Free boundary problems; Fractional derivatives and integrals;

D O I：

10.1016/j.cam.2022.114470

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a Caputo time fractional degenerate diffusion equation which we prove to be equivalent to the fractional parabolic obstacle problem, showing that its solution evolves for any alpha is an element of (0, 1) to the same stationary state, the solution of the classic elliptic obstacle problem. The only thing which changes with alpha is the convergence speed. We also study the problem from the numerical point of view, comparing some finite different approaches, and showing the results of some tests. These results extend what recently proved in [ 1] for the case alpha = 1. (C) 2022 Elsevier B.V. All rights reserved.

引用

页数：11

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