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 quasilinear hyperbolic systems of diagonal form with weakly linearly degenerate characteristic fields. On the basis of global existence and uniqueness of C1 solution, we prove that the solution to the Cauchy problem approaches a combination of C1 traveling wave solutions when t tends to the infinity.