Viscous Shock Wave and Boundary Layer Solution to an Inflow Problem for Compressible Viscous Gas.

The inflow problem for a one-dimensional compressible viscous gas on the half line (0,+∞) is investigated. The asymptotic stability on both the viscous shock wave and a superposition of the viscous shock wave and the boundary layer solution is established under some smallness conditions. The proofs are given by an elementary energy method. [ABSTRACT FROM AUTHOR]