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

Feimin Huang, Akiataka Matsumura, and Xiaoding Shi

Abstract: The inflow problem for a one-dimensional compressible viscous gas on the half line (0,+$\infty)$ 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.

Paper:
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Author(s):
Feimin Huang, <fhuang@math.sci.osaka-u.ac.jp>
Akiataka Matsumura, <akiataka@math.sci.osaka-u.ac.jp>
Xiaoding Shi, <shixd@math.sci.osaka-u.ac.jp>
Publishing information:
Submitted to Comm.Math.Phys.