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Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas

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Abstract

This paper is concerned with the asymptotic behavior toward the rarefaction waves of the solution of a one-dimensional model system associated with compressible viscous gas. If the initial data are suitably close to a constant state and their asymptotic values atx=±∞ are chosen so that the Riemann problem for the corresponding hyperbolic system admits the weak rarefaction waves, then the solution is proved to tend toward the rarefaction waves ast→+∞. The proof is given by an elementaryL 2 energy method.

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Kyoto University, 606, Kyoto, Japan

    Akitaka Matsumura

  2. Tokyo National Technical College, Hachioji, 193, Tokyo, Japan

    Kenji Nishihara

Authors
  1. Akitaka Matsumura
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  2. Kenji Nishihara
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Matsumura, A., Nishihara, K. Asymptotics toward the rarefaction waves of the solutions of a one-dimensional model system for compressible viscous gas. Japan J. Appl. Math. 3, 1–13 (1986). https://doi.org/10.1007/BF03167088

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  • DOI: https://doi.org/10.1007/BF03167088

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