Long time behavior of non-Fickian delay reaction-diffusion equations

被引：35
作者：
Li, Dongfang [1 ]
Zhang, Chengjian [1 ]
Wang, Wansheng [2 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[2] Changsha Univ Sci & Technol, Sch Math & Computat Sci, Changsha 410114, Hunan, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2012年 / 13卷 / 03期
关键词：
Non-Fickian delay reaction-diffusion equations; Energy estimates; Stability; Contractivity; Numerical methods; Biological models; VOLTERRA INTEGRODIFFERENTIAL EQUATIONS; FUNCTIONAL-DIFFERENTIAL EQUATIONS; RUNGE-KUTTA METHODS; ASYMPTOTIC STABILITY; DYNAMICAL-SYSTEMS; DISSIPATIVITY; WAVES;
D O I：
10.1016/j.nonrwa.2011.11.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the long time behavior of non-Fickian delay reaction-diffusion equations. These kinds of Volterra integro-differential equations are derived by combining a time memory term in the flux and a delay parameter in the reaction term. Energy estimates, dissipativity, asymptotic stability, and contractivity of the problems are obtained. Moreover, we prove that the numerical method discussed in the present paper has the ability to preserve stability and contractivity of the underlying systems. Some confirmations of these are illustrated by using the numerical method on two biological models. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1401 / 1415
页数：15
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