期刊论文

Xiang, Jianlin

英文

数学物理学报(英文版)

0252-9602

2015

35

6

1325-1338

10.1016/S0252-9602(15)30057-6

∗Received September 3, 2014; revised November 24, 2014. 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). †Corresponding author: Jianlin XIANG.

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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 a and ν by the method of energy estim...