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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Osaka University, Osaka, 560-0045, Japan

    Feimin Huang, Akitaka Matsumura & Xiaoding Shi

  2. Institute of Applied Mathematics, AMSS, Academia Sinica, Beijing, 100080, P.R. China

    Feimin Huang

  3. Department of Mathematics and Information Science, Beijing University of Chemical Technology, Beijing, 100029, P.R. China

    Xiaoding Shi

Authors
  1. Feimin Huang
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  2. Akitaka Matsumura
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  3. Xiaoding Shi
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Correspondence to Akitaka Matsumura.

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Huang, F., Matsumura, A. & Shi, X. Viscous Shock Wave and Boundary Layer Solution to an Inflow Problem for Compressible Viscous Gas. Commun. Math. Phys. 239, 261–285 (2003). https://doi.org/10.1007/s00220-003-0874-9

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  • DOI: https://doi.org/10.1007/s00220-003-0874-9

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