Asymptotic behaviour of travelling waves for the delayed Fisher-KPP equation

被引：31

作者：

Ducrot, Arnaud ^{[1
,2
]}

Nadin, Gregoire ^{[3
,4
]}

机构：

[1] Univ Bordeaux, IMB, UMR 5251, F-33076 Bordeaux, France

[2] CNRS, IMB, UMR 5251, F-33400 Talence, France

[3] Univ Paris 06, Lab Jacques Louis Lions, F-75005 Paris, France

[4] CNRS, UMR 7598, F-75005 Paris, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年 / 256卷 / 09期

基金：

欧洲研究理事会;

关键词：

Travelling wave solutions; Time delay; Maximal wavetrain; Oscillations; REACTION-DIFFUSION EQUATION; SYSTEMS;

D O I：

10.1016/j.jde.2014.01.033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work we study the behaviour of travelling wave solutions for the diffusive Hutchinson equation with time delay. Using a phase plane analysis we prove the existence of travelling wave solution for each wave speed c >= 2. We show that for each given and admissible wave speed, such travelling wave solutions converge to a unique maximal wavetrain. As a consequence the existence of a nontrivial maximal wavetrain is equivalent to the existence of travelling wave solution non-converging to the stationary state u = 1. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：3115 / 3140

页数：26

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