Asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems

This paper is concerned with the asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems with linearly degenerate characteristic fields. Based on the existence results of global classical solutions, we prove that when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that L1 (intersection)L(omega) norm of the initial data as well as its derivative are bounded. Application is given for the time-like extremal surface in Minkowski space.