Shock waves for a model system of the radiating gas

Shuichi Kawashima, Shinya Nishibata

    Research output: Contribution to journalArticlepeer-review

    87 Citations (Scopus)

    Abstract

    This paper is concerned with the existence and the asymptotic stability of traveling waves for a model system derived from approximating the one-dimensional system of the radiating gas. We show the existence of smooth or discontinuous traveling waves and also prove the uniqueness of these traveling waves under the entropy condition, in the class of piecewise smooth functions with the first kind discontinuities. Furthermore, we show that the C3-smooth traveling waves are asymptotically stable and that the rate of convergence toward these waves is t-1/4, which looks optimal. The proof of stability is given by applying the standard energy method to the integrated equation of the original one.

    Original languageEnglish
    Pages (from-to)95-117
    Number of pages23
    JournalSIAM Journal on Mathematical Analysis
    Volume30
    Issue number1
    DOIs
    Publication statusPublished - 1998

    All Science Journal Classification (ASJC) codes

    • Analysis
    • Computational Mathematics
    • Applied Mathematics

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