Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas

Akitaka Matsumura, Kenji Nishihara

    Research output: Contribution to journalArticle

    128 Citations (Scopus)

    Abstract

    This paper is concerned with the asymptotic behavior toward the rarefaction wave of the solution of a one-dimensional barotropic model system for compressible viscous gas. We assume that the initial data tend to constant states at x=±∞, respectively, and the Riemann problem for the corresponding hyperbolic system admits a weak continuous rarefaction wave. If the adiabatic constant γ satisfies 1≦γ≦2, then the solution is proved to tend to the rarefaction wave as t→∞ under no smallness conditions of both the difference of asymptotic values at x=±∞ and the initial data. The proof is given by an elementary L2-energy method.

    Original languageEnglish
    Pages (from-to)325-335
    Number of pages11
    JournalCommunications in Mathematical Physics
    Volume144
    Issue number2
    DOIs
    Publication statusPublished - 1992 Feb

    Fingerprint

    Rarefaction Wave
    One-dimensional Model
    Global Stability
    elastic waves
    gases
    Tend
    hyperbolic systems
    energy methods
    Cauchy problem
    Energy Method
    Hyperbolic Systems
    Cauchy Problem
    Asymptotic Behavior
    Gas

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Physics and Astronomy(all)
    • Mathematical Physics

    Cite this

    Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas. / Matsumura, Akitaka; Nishihara, Kenji.

    In: Communications in Mathematical Physics, Vol. 144, No. 2, 02.1992, p. 325-335.

    Research output: Contribution to journalArticle

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