Stability of periodic Kuramoto-Sivashinsky waves

被引：16

作者：

Barker, Blake ^{[1
]}

Johnson, Mathew A. ^{[2
]}

Noble, Pascal

Rodrigues, L. Miguel ^{[3
]}

Zumbrun, Kevin ^{[1
]}

机构：

[1] Indiana Univ, Bloomington, IN 47405 USA

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

[3] Univ Lyon 1, Inst Camille Jordan, UMR CNRS 5208, F-69622 Villeurbanne, France

来源：

APPLIED MATHEMATICS LETTERS | 2012年 / 25卷 / 05期

基金：

美国国家科学基金会;

关键词：

Periodic waves; Kuramoto-Sivashinsky equations; Modulational stability; VISCOUS CONSERVATION-LAWS; NONLINEAR STABILITY;

D O I：

10.1016/j.aml.2011.10.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of decay. The approach extends readily to other second- and higher-order parabolic equations, for example, the Cahn Hilliard equation or more general thin film models. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：824 / 829

页数：6

共 18 条

[1]

Barker B., 2011, NONLINEAR MODULATION

[2]

Barker B., 2010, P SEM CTR M IN PRESS

[3] Stability of compressive and undercompressive thin film travelling waves [J].