Existence and Non-Existence of Fisher-KPP Transition Fronts

被引：64

作者：

Nolen, James ^{[1
]}

Roquejoffre, Jean-Michel ^{[2
]}

Ryzhik, Lenya ^{[3
]}

Zlatos, Andrej ^{[4
]}

机构：

[1] Duke Univ, Dept Math, Durham, NC 27708 USA

[2] Univ Toulouse 3, Inst Math, UMR CNRS 5219, F-31062 Toulouse, France

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[4] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2012年 / 203卷 / 01期

基金：

美国国家科学基金会;

关键词：

DIFFUSION EQUATIONS; GENERALIZED FRONTS;

D O I：

10.1007/s00205-011-0449-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global-in-time solutions while creating a global-in-time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized inhomogeneity leads to the existence of transition fronts, but only in a finite range of speeds. These results are in contrast with both Fisher-KPP reactions in homogeneous media as well as ignition-type reactions in inhomogeneous media.

引用

页码：217 / 246

页数：30

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