Asymptotic behavior of global classical solutions to Goursat problem of quasilinear hyperbolic systems

This work is concerned with the asymptotic behavior of global C 1 solutions of the Goursat problem for quasilinear hyperbolic systems. We prove that when t tends to the infinity, the solutions approach a combination of C 1 traveling wave solutions at algebraic rate ( 1 + t ) − μ , provided that the boundary data decay at the rate ( 1 + t ) − ( 1 + μ ) , where μ is a positive constant. Finally, we give an application to the equation for motion of an elastic string.