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This paper is concerned with the inflow problem for the one-dimensionalcompressible Navier-Stokes equations. For such a problem, F. M. Huang, A.Matsumura and X. D. Shi showed that there exists viscous shock wave solution tothe inflow problem and both the boundary layer solution, the viscous shockwave, and their superposition are time-asymptotically nonlinear stable undersmall initial perturbation. The main purpose of this paper is to show thatsimilar stability results still hold for a class of large initial perturbationwhich can allow the initial density to have large oscillations. The proofs aregiven by an elementary energy method and the key point is to deduce the desireduniform positive lower and upper bounds on the density.

Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations