STABILITY OF NON-MONOTONE NON-CRITICAL TRAVELING WAVES IN DISCRETE REACTION-DIFFUSION EQUATIONS WITH TIME DELAY

被引：12

作者：

Yang, Zhao-Xing ^{[1
]}

Zhang, Guo-Bao ^{[1
]}

Tian, Ge ^{[1
]}

Feng, Zhaosheng ^{[2
]}

机构：

[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Gansu, Peoples R China

[2] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2017年 / 10卷 / 03期

关键词：

NICHOLSONS BLOWFLIES EQUATION; SPREADING SPEEDS; MONOSTABLE EQUATIONS; ASYMPTOTIC STABILITY; FRONTS; UNIQUENESS; EXISTENCE; DYNAMICS;

D O I：

10.3934/dcdss.2017029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with traveling waves for temporally delayed, spatially discrete reaction-diffusion equations without quasi-monotonicity. We first establish the existence of non-critical traveling waves (waves with speeds c > c*, where c* is minimal speed). Then by using the weighted energy method with a suitably selected weight function, we prove that all noncritical traveling waves phi(x + ct) (monotone or nonmonotone) are time asymptotically stable, when the initial perturbations around the wavefronts in a certain weighted Sobolev space are small.

引用

页码：581 / 603

页数：23

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