Asymptotic behavior of classical solutions of reducible quasilinear hyperbolic systems with characteristic boundaries

In this paper, we investigate the asymptotic behavior of classical solutions of reducible quasilinear hyperbolic systems with characteristic boundaries. Under some suitable assumptions, we prove that the solution approaches a combination of Lipschitz continuous and piecewise C 1 traveling wave solution. As an application, we apply the result to the equation for time-like extremal surfaces in the Minkowski space–time R 1 + ( 1 + n ) .