Time-delayed reaction-diffusion equations with boundary effect: (I) convergence to non-critical traveling waves
Time-delayed reaction-diffusion equations with boundary effect: (I) convergence to non-critical traveling waves
复制标题
具有边界效应的时滞反应扩散方程：（I）收敛到非临界行波
DOI：
10.1080/00036811.2016.1258696
复制
发表时间：
2018
影响因子：
1.1
通讯作者：
Zhang Kaijun
中科院分区：
文献类型：
--
作者：
Jiang Yicheng;Zhang Kaijun
研究半空间上具有边界效应的时滞反应扩散方程。当出生率函数为非单调函数时，证明了在适当的边界条件下，时滞方程的解时间指数收敛于某个（单调或非单调）行波剖面与波速，其中是最小波速，当初始数据是波周围的小扰动时，而波远离边界移动，使得边界层足够小。采用的方法是技术加权能量法，并对边界项进行了一些新的处理。然而，当所考虑的出生率函数是单调的，那么，对于所有的行波，无论边界层的大小，这些单调行波总是全局稳定的。证明方法是单调技术和挤压定理，但有一些新的发展。
This paper is concerned with time-delayed reaction–diffusion equations on half space with boundary effect. When the birth rate function is non-monotone, the solution of the delayed equation subjected to appropriate boundary condition is proved to converge time-exponentially to a certain (monotone or non-monotone) traveling wave profile with wave speed, where is the minimum wave speed, when the initial data is a small perturbation around the wave, while the wave is shifted far away from the boundary so that the boundary layer is sufficiently small. The adopted method is the technical weighted-energy method with some new flavors to handle the boundary terms. However, when the birth rate function is monotone under consideration, then, for all traveling waves with, no matter what size of the boundary layers is, these monotone traveling waves are always globally stable. The proof approach is the monotone technique and squeeze theorem but with some new development.