Global classical discontinuous solutions to a class of generalized Riemannproblem for general quasilinear hyperbolic systems of conservation laws

In this paper, the authors prove the global existence and uniqueness of pie cewise C-1 solution u = u(t, x) containing only n contact discontinuities w ith small amplitude to the generalized Riemann problem for general linearly degenerate quasilinear hyperbolic systems of conservation laws with small decay initial data. This solution has a global structure similar to the sim ilarity solution u = U(x/t) to the corresponding Riemann problem. The resul t shows that the similarity solution u = U(x/t) possesses a global nonlinea r structural stability.