Acta mathematica scientia, Series B >
ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM
Received date: 2014-11-24
Revised date: 2014-09-03
Online published: 2015-11-01
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).
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.
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 . DOI: 10.1016/S0252-9602(15)30057-6
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