  In this paper, the asymptotic-time behavior of solutions to an initial
boundary value problem in the half space for 1-D isentropic Navier-Stokes
system is investigated. It is shown that the viscous shock wave is stable for
an impermeable wall problem where the velocity is zero on the boundary provided
that the shock wave is initially far away from the boundary. Moreover, the
strength of shock wave could be arbitrarily large. This work essentially
improves the result of [A. Matsumura, M. Mei, Convergence to travelling fronts
of solutions of the p-system with viscosity in the presence of a boundary,
Arch. Ration. Mech. Anal., 146(1): 1-22, 1999], where the strength of shock
wave is sufficiently small.
