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

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)-μ, provided that the initial data decay with the rate (1 + x)-(1+μ) (resp. (1 x)-(1+μ)) as x tends to +∞ (resp. -∞), where μ is a positive constant.