MULTIDIMENSIONAL STABILITY OF TRAVELING WAVES IN A BISTABLE REACTION-DIFFUSION EQUATION .2.

被引：74

作者：

LEVERMORE, CD ^{[1
]}

XIN, JX ^{[1
]}

机构：

[1] MATH SCI RES INST,BERKELEY,CA 94720

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 1992年 / 17卷 / 11-12期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1080/03605309208820908

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the planar traveling wave solutions of a bistable reaction-diffusion equation are stable in L(loc)2(R(n)) for n greater-than-or-equal-to 2, provided the initial perturbation is small and localized in some sense. In order to obtain control on the perturbation globally in time, we estimate lower bounds of a Lyapunov functional using the maximum principle, and spectral theory.

引用

页码：1901 / 1924

页数：24

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