非局部时滞反应扩散方程波前解的指数稳定性  

Exponential Stability of Traveling Wavefronts for Reaction-Diffusion Equations With Delayed Nonlocal Responses

作　　者：李盼晓 LI Panxiao(School of Mathematics and Statistics,Xidian University,Xi＇an 710071,P.R.China)

机构地区：[1]西安电子科技大学数学与统计学院,西安710071

出　　处：《应用数学和力学》2018年第11期1300-1312,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11671315)~~

摘　　要：该文考虑了一类具有非局部时滞反应项的空间非局部扩散模型,主要研究其波前解的渐近稳定性及收敛率.通过构造加权函数,建立了相关线性方程的比较原理,证明了当初始扰动在加权最大范数意义下一致有界,满足初值问题的解将依时间指数收敛到波前解,而且得到其指数收敛率.A spatially nonlocal diffusion model with a class of delayed nonlocal responses was considered. The asymptotic stability and the convergence rate of the traveling wavefronts were mainly studied. Through construction of weighted functions and establishment of a comparison principle for the related linear equations, the conclusion that if the initial function is within a bounded distance from a certain traveling wavefront with respect to a weighted maximum norm, the solution satisfying the initial value will converge to the traveling wavefront exponentially in time, was proved, and the exponential convergence rate was also obtained.

关 键 词：行波解 非局部时滞 稳定性 

分 类 号：O175.14[理学—数学]