Asymptotic Behavior Of Global Classical Solutions To Quasilinear Hyperbolic Systems Of Diagonal Form

This paper deals with the asymptotic behavior of global classical solutions to qua-silinear hyperbolic systems of diagonal form with weakly linearly degenerate characteristic fields. Based on the global existence and uniqueness of C~1 solution, we prove that the solution to the cauchy problem approaches a combination of C~1 traveling wave solutions when t tends to the infinity.