On a time fractional reaction diffusion equation

被引：31

作者：

Ahmad, B. ^{[1
]}

Alhothuali, M. S. ^{[1
]}

Alsulami, H. H. ^{[1
]}

Kirane, M. ^{[2
]}

Timoshin, S. ^{[3
]}

机构：

[1] King Abdulaziz Univ, Dept Math, Fac Sci, Jeddah 21589, Saudi Arabia

[2] Univ La Rochelle, Lab Math Images & Applicat, Pole Sci & Technol, F-17031 La Rochelle, France

[3] UCL, Dept Math, London WC1E 6BT, England

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 257卷

关键词：

Reaction-diffusion equation; Caputo fractional derivative; Global existence; Blow-up;

D O I：

10.1016/j.amc.2014.06.099

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A reaction diffusion equation with a Caputo fractional derivative in time and with various boundary conditions is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions will be analyzed. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：199 / 204

页数：6

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