Asymptotic behavior of solutions for a degenerate hyperbolic system of viscous conservation laws with boundary effect

This paper studies the asymptotic behavior of solutions to the initial boundary value problem on the half space R+ a 2 x 2 degenerate system of viscous conservation laws. We show that the solution of the IBVP exists globally in time and tends toward a shifted critical viscous shock wave as time goes to infinity. We also prove that the system does not exhibit "phase transition" and remains in the degenerate hyperbolic state, when the initial perturbations are small. The proof is given by a weighted energy method.