Invariant sets and solutions to the two-dimensional nonlinear reaction–diffusion equations

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• 作者：Chunrong Zhu ; Changzheng Qu ; Shunli Zhang
• 关键词：Reaction– ; diffusion equation ; Exact solution ; Invariant set ; Interfaces
• 刊名：Nonlinear Analysis
• 出版年：2009
• 出版时间：15 December 2009
• 年：2009
• 卷：71
• 期：12
• 页码：e1139-e1152
• 全文大小：361 K

文摘

In this paper we utilize the method of invariant set to derive exact solutions of the two-dimensional nonlinear reaction–diffusion equations with source term. It is shown that there exists a class of reaction–diffusion equations which are invariant with respect to the sets and , with f≠g. As a result, we obtain exact solutions of the certain nonlinear reaction–diffusion equations. These solutions extend the well-known self-similar solutions and instantaneous source type solutions of the porous medium equation. The behavior to some solutions and the corresponding interfaces are also described.