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

This work is concerned with the asymptotic behavior of global C1C1 solutions of the Goursat problem for quasilinear hyperbolic systems. We prove that when tt tends to the infinity, the solutions approach a combination of C1C1 traveling wave solutions at algebraic rate (1+t)−μ(1+t)−μ, provided that the boundary data decay at the rate (1+t)−(1+μ)(1+t)−(1+μ), where μμ is a positive constant. Finally, we give an application to the equation for motion of an elastic string.