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.
基金
Supported by the National Natural Science Foundation of China (Grant No.10771038)