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Asymptotic stability of solutions with a single strong shock wave for hyperbolic systems of conservation laws

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Abstract

We consider the large-time behavior of solutions for general hyperbolic systems of conservation laws with initial data containing a single strong discontinuity. This problem is to study the asymptotic behavior of a single strong shock wave interacting with weak waves. Stability and truncation error analysis for the Glimm scheme applied to solve these initial-value problems were studied by I.L. Chern. We shall show that under the Chern stability condition the strength and the speed of the strong shock wave approach those of an entropy shock at the ratet −3/2 and the total variation of the solution outside of the strong shock approaches zero at the ratet −1/2.

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Authors and Affiliations

  1. Faculty of Economics, Otemon-Gakuin University, 2-1-15 Nishiai, 567, Ibaraki-city, Osaka, Japan

    Fumioki Asakura

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  1. Fumioki Asakura
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Asakura, F. Asymptotic stability of solutions with a single strong shock wave for hyperbolic systems of conservation laws. Japan J. Indust. Appl. Math. 11, 225–244 (1994). https://doi.org/10.1007/BF03167223

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  • DOI: https://doi.org/10.1007/BF03167223

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