Asymptotic Behavior of Global Classical Solutions to the Cauchy Problem on a Semi-Bounded Initial Axis for Quasilinear Hyperbolic Systems  

作　　者：Wei Wei HAN1,2 1. Department of Applied Mathematics, Donghua University, Shanghai 201620, P. R. China 2. School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China 

出　　处：《Journal of Mathematical Research and Exposition》2010年第1期41-53,共13页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10771038)

摘　　要：In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.

关 键 词：quasilinear hyperbolic system Cauchy problem on a semi-bounded initial axis global classical solution weak linear degeneracy matching condition travelling wave. 

分 类 号：O175.22[理学—数学]