Rapid traveling waves in the nonlocal Fisher equation connect two unstable states

被引：64

作者：

Alfaro, Matthieu ^{[1
]}

Coville, Jerome ^{[2
]}

机构：

[1] Univ Montpellier 2, I3M, F-34095 Montpellier 5, France

[2] INRA, Equipe BIOSP, F-84914 Avignon 9, France

来源：

APPLIED MATHEMATICS LETTERS | 2012年 / 25卷 / 12期

关键词：

Integro-differential equation; Traveling waves; Turing instability; FRONTS;

D O I：

10.1016/j.aml.2012.05.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

In this note, we give a positive answer to a question addressed in Nadin et al. (2011)[7]. To be precise, we prove that, for any kernel and any slope at the origin, there exist traveling wave solutions (actually those which are "rapid") of the nonlocal Fisher equation that connect the two homogeneous steady states 0 (dynamically unstable) and 1. In particular, this allows situations where 1 is unstable in the sense of Turing. Our proof does not involve any maximum principle argument and applies to kernels with fat tails. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：2095 / 2099

页数：5

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