STABILITY OF A PLANAR FRONT IN A CLASS OF REACTION-DIFFUSION SYSTEMS

被引：2

作者：

Ghazaryan, A. ^{[1
]}

Latushkin, Y. ^{[2
]}

Yang, X. ^{[3
]}

机构：

[1] Miami Univ, Dept Math, Oxford, OH 45056 USA

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[3] Xian Jiaotong Liverpool Univ, Dept Math Sci, Suzhou 215123, Jiangsu, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 05期

基金：

美国国家科学基金会;

关键词：

traveling waves; fronts; planar fronts; stability; nonlinear stability; essential spectrum; convective instability; exponential weights; TRAVELING-WAVE SOLUTIONS; MULTIDIMENSIONAL STABILITY; ASYMPTOTIC STABILITY; PARABOLIC-SYSTEMS; COMBUSTION; INSTABILITIES; EQUATION; MODEL;

D O I：

10.1137/17M1161592

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear level, the spectrum is stabilized by using an exponential weight. A priori estimates for the nonlinear terms of the equation governing the evolution of the perturbations of the front are obtained when perturbations belong to the intersection of the exponentially weighted space with the original space without a weight. These estimates are then used to show that in the original norm, initially small perturbations to the front remain bounded, while in the exponentially weighted norm, they algebraically decay in time.

引用

页码：5569 / 5615

页数：47

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[3]

[Anonymous], ELECT J COMBIN

[4]

[Anonymous], 2002, APPL MATH SCI