Viscous shock wave and boundary layer solution to an inflow problem for compressible viscous gas
The authors examine the inflow problem for a one-dimensional compressible viscous gas on the semi-axis \(x\in (0,+\infty)\). The asymptotic stability of both the viscous shock wave and a superposition of the viscous shock wave and boundary layer solution is established under some smallness conditions, provided the viscous shock profile is sufficiently far from the boundary initially. The proofs are based on the reformulation of the original problem as an initial-boundary value problem, on the Leray-Schauder fixed point theorem and a priori energy estimates.
scientific article; zbMATH DE number 1969279