ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM

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

Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (6): 1325-1338.doi: 10.1016/S0252-9602(15)30057-6

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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).

Abstract

Abstract:

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.

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

CLC Number:

35K45

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

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