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

被引：6
|
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：
欧洲研究理事会; 美国国家科学基金会;
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].
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页码：2473 / 2496
页数：24
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