Multidimensional stability of traveling fronts in monostable reaction-diffusion equations with complex perturbations

被引：10
|
作者：
Zeng HuiHui [1 ]
机构：
[1] Tsinghua Univ, Ctr Math Sci, Beijing 100084, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2014年 / 57卷 / 02期
基金：
美国国家科学基金会;
关键词：
traveling fronts; reaction-diffusion equations; multi-dimensional stability; NONLINEAR STABILITY; WAVES;
D O I：
10.1007/s11425-013-4617-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper studies the multidimensional stability of traveling fronts in monostable reaction-diffusion equations, including Ginzburg-Landau equations and Fisher-KPP equations. Eckmann andWayne (1994) showed a one-dimensional stability result of traveling fronts with speeds c a (c) 1/2 c (*) (the critical speed) under complex perturbations. In the present work, we prove that these traveling fronts are also asymptotically stable subject to complex perturbations in multiple space dimensions (n = 2, 3), employing weighted energy methods.
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页码：353 / 366
页数：14
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