ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM

doi:10.1016/S0252-9602(15)30057-6

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (6): 1325-1338.doi: 10.1016/S0252-9602(15)30057-6

ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM

蒋咪娜, 向建林

1. The Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
2. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430079, China

收稿日期:2014-11-24 修回日期:2014-09-03 出版日期:2015-11-01 发布日期:2015-11-01
通讯作者: Jianlin XIANG, E-mail: jlxiang2@163.com E-mail:jlxiang2@163.com
作者简介:Mina JIANG, E-mail: jmn3911@mail.ccnu.edu.cn
基金资助:
Jiang's research was supported by the Natural Science Foundation of China (11001095), the Ph.D. specialized grant of the Ministry of Education of China (20100144110001) and the Special Fund for Basic Scientific Research of Central Colleges (CCNU12C01001). Xiang's research was supported by the Fundamental Research Funds for the Central Universities (2015IA009) and the Natural Science Foundation of China (61573012).

ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM

Mina JIANG, Jianlin XIANG

1. The Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
2. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430079, China

Received:2014-11-24 Revised:2014-09-03 Online:2015-11-01 Published:2015-11-01
Contact: Jianlin XIANG, E-mail: jlxiang2@163.com E-mail:jlxiang2@163.com
Supported by:
Jiang's research was supported by the Natural Science Foundation of China (11001095), the Ph.D. specialized grant of the Ministry of Education of China (20100144110001) and the Special Fund for Basic Scientific Research of Central Colleges (CCNU12C01001). Xiang's research was supported by the Fundamental Research Funds for the Central Universities (2015IA009) and the Natural Science Foundation of China (61573012).

摘要/Abstract

摘要：

This paper is concerned with the existence and the nonlinear asymptotic stability of traveling wave solutions to the Cauchy problem for a system of dissipative evolution equations

with initial data and end states
(ξ, θ)(x, 0) = (ξ₀, θ₀)(x)→ (ξ_±, θ_±) as x→±∞.
We obtain the existence of traveling wave solutions by phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without restrictions on the coefficients α and v by the method of energy estimates.

关键词: dissipative evolution equations, traveling wave solutions, nonlinear stability, energy estimates

Abstract:

Key words: dissipative evolution equations, traveling wave solutions, nonlinear stability, energy estimates

中图分类号:

35K45

蒋咪娜, 向建林. ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM[J]. 数学物理学报(英文版), 2015, 35(6): 1325-1338.

Mina JIANG, Jianlin XIANG. ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM[J]. Acta mathematica scientia,Series B, 2015, 35(6): 1325-1338.

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ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM

ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM

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