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In this paper, the asymptotic-time behavior of solutions to an initialboundary value problem in the half space for 1-D isentropic Navier-Stokessystem is investigated. It is shown that the viscous shock wave is stable foran impermeable wall problem where the velocity is zero on the boundary providedthat the shock wave is initially far away from the boundary. Moreover, thestrength of shock wave could be arbitrarily large. This work essentiallyimproves the result of [A. Matsumura, M. Mei, Convergence to travelling frontsof 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 shockwave is sufficiently small.

Stability of Large Amplitude Viscous Shock Wave for 1-D Isentropic Navier-Stokes System in the Half Space