  In this paper, a viscous shock wave under space-periodic perturbation of 1-D
isentropic Navier-Stokes system in the half space is investigated. It is shown
that if the initial periodic perturbation around the viscous shock wave is
small, then the solution time asymptotically tends to a viscous shock wave with
a shift partially determined by the periodic oscillations. Moreover, the
strength of {the} shock wave could be arbitrarily large. This result
essentially improves the previous work " 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 (1999), no. 1, 1-22." where the
strength of shock wave is sufficiently small and the initial periodic
oscillations vanish.
