MULTIDIMENSIONAL STABILITY OF PLANAR TRAVELING WAVES FOR THE SCALAR NONLOCAL ALLEN-CAHN EQUATION

被引：9

作者：

Faye, Gregory ^{[1
,2
]}

机构：

[1] CAMS Ecole Hautes Etud Sci Soci, F-75013 Paris, France

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

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 05期

基金：

美国国家科学基金会; 欧洲研究理事会;

关键词：

Nonlocal equation; traveling wave; nonlinear stability; REACTION-DIFFUSION EQUATION; VISCOUS CONSERVATION-LAWS; ASYMPTOTIC-BEHAVIOR; EVOLUTION-EQUATIONS; SPECTRAL-ANALYSIS; MODEL;

D O I：

10.3934/dcds.2016.36.2473

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the multidimensional stability of planar traveling waves for scalar nonlocal Allen-Cahn equations using semigroup estimates. We show that if the traveling wave is spectrally stable in one space dimension, then it is stable in n-space dimension, n >= 2, with perturbations of the traveling wave decaying like t(-(n-1)/4) as t -> +infinity in H-k(R-n) for k >= [n+1/2].

引用

页码：2473 / 2496

页数：24

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