STABILITY OF TRAVELING WAVES FOR NONLOCAL TIME-DELAYED REACTION-DIFFUSION EQUATIONS

被引：3
|
作者：
Jiang, Yicheng [1 ]
Zhang, Kaijun [1 ]
机构：
[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
来源：
KINETIC AND RELATED MODELS | 2018年 / 11卷 / 05期
关键词：
Traveling wave; time delay; nonlocal reaction-diffusion equations; L-2-weighted energy; stability; NICHOLSONS BLOWFLIES EQUATION; FRONTS; NONLINEARITY;
D O I：
10.3934/krm.2018048
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the stability of noncritical/critical traveling waves for nonlocal time-delayed reaction-diffusion equation. When the birth rate function is non-monotone, the solution of the delayed equation is proved to converge time-exponentially to some (monotone or non-monotone) traveling wave profile with wave speed c > c(*), where c(*) > 0 is the minimum wave speed, when the initial data is a small perturbation around the wave. However, for the critical traveling waves (c = c(*)), the time-asymptotical stability is only obtained, and the decay rate is not gotten due to some technical restrictions. The proof approach is based on the combination of the anti-weighted method and the nonlinear Halanay inequality but with some new development.
引用
收藏
页码：1235 / 1253
页数：19
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