Diffusion in Allen-Cahn equation: Normal vs anomalous

被引：5
|
作者：
Fan, Enyu [1 ]
Li, Changpin [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2024年 / 457卷
基金：
中国国家自然科学基金;
关键词：
Allen-Cahn equation; Fractional derivative; L1; formula; LOGARITHMIC CREEP LAW; SCHEME;
D O I：
10.1016/j.physd.2023.133973
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is known that the anomalous diffusion can be well characterized by the fractional derivatives. In this paper, the Allen-Cahn equations with different kinds of time fractional derivatives are numerically studied. The numerical solutions of the Allen-Cahn equations are obtained by using Euler method or L1 method to approximate the time derivative and the finite element method in the space direction. Finally, the influences of time derivatives on the solutions of the considered models are observed and discussed.
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收藏
页数：15
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