Quenching phenomenon of a time-fractional diffusion equation with singular source term

被引：10
|
作者：
Xu, Yufeng [1 ]
Zheng, Zhoushun [1 ]
机构：
[1] Cent S Univ, Dept Appl Math, Changsha 410083, Hunan, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 16期
基金：
中国博士后科学基金;
关键词：
quenching phenomenon; fractional diffusion equation; finite difference method; numerical simulation; DIFFERENTIAL-EQUATIONS;
D O I：
10.1002/mma.4424
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a time-fractional diffusion equation with singular source term is considered. The Caputo fractional derivative with order 0 < alpha <= 1 is applied to the temporal variable. Under specific initial and boundary conditions, we find that the time-fractional diffusion equation presents quenching solution that is not globally well-defined as time goes to infinity. The quenching time is estimated by using the eigenfunction of linear fractional diffusion equation. Moreover, by implementing a finite difference scheme, we give some numerical simulations to demonstrate the theoretical analysis. Copyright (c) 2017 John Wiley & Sons, Ltd.
引用
收藏
页码：5750 / 5759
页数：10
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