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

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• 作者：Dongfang Li^a ; ^{hustldf@gmail.com} ; Chengjian Zhang^a ; ^{cjzhang@mail.hust.edu.cn} ; Wansheng Wang^b ; ^{w.s.wang@163.com}
• 关键词：Non-Fickian delay reaction&ndash ; diffusion equations ; Energy estimates ; Stability ; Contractivity ; Numerical methods ; Biological models
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：13
• 期：3
• 页码：1401-1415
• 全文大小：521 K

文摘

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.