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:**- Available as PostScript (336 Kbytes) or gzipped PostScript (128 Kbytes; uncompress using gunzip).
**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.
**Comments:****Submitted by:**- <fhuang@math.sci.osaka-u.ac.jp> June 13 2002.

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