Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary

We study the asymptotic behavior as time goes to innity of solutions to the initial-boundary-value problem on the half space RC for a one-dimensional model system for the isentropic ow of a compressible viscous gas, the so-calledp-system with viscosity. As boundary conditions, we prescribe the constant state at innity and require that the velocity be zero at the boundary x D 0. When the velocity at innity is negative and satises a condition on the magnitude, we prove that if the initial data are suitably close to those for the corresponding outgoing viscous shock prole, which is suitably far from the boundary, then a unique solution exists globally in time and tends toward the properly shifted viscous shock prole as th