Global exponential stability of traveling waves in monotone bistable systems
Global exponential stability of traveling waves in monotone bistable systems
复制标题
DOI：
10.3934/dcds.2008.21.601
复制
发表时间：
2008-03
影响因子：
1.1
通讯作者：
J. Tsai
中科院分区：
文献类型：
--
作者：
J. Tsai
研究了一类扩散系数为零的一般单调反应扩散方程组行波解的渐近指数稳定性。得到这些结果的主要工具是比较原理、适当构造的上下解和压缩方法。不需要对与所研究的行波解相关的线性算子进行谱分析。因此，我们的结果不仅恢复和/或补充了文献中较早的稳定性结果，而且提供了一种简单的方法来证明具有正扩散系数的一般单调反应扩散时滞系统行波解的渐近指数稳定性.
We study the asymptotic exponential stability of traveling front solutions for a general monotone reaction-diffusion bistable system with some diffusion coefficients being zero. The main tools to obtain our results are comparison principle, suitably constructed super-sub solutions, and squeezing methods. No spectrum analysis of the linear operator associated with traveling front solutions under study is needed. Therefore, our results not only recover and/or complement earlier stability results in the literature, but also provide a simple method to show the asymptotic exponential stability of traveling front solutions for a general monotone reaction-diffusion bistable system with positive diffusion coefficients.