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Free boundary value problem of the one-dimensional model of polytropic ideal gas

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Abstract

In this paper the free boundary value problem of the one-dimensional model of polytropic ideal gas is discussed. Under some smallness assumption on the initial data, the global weak solution of our problem is obtained. Furthermore the solution decays inL ∞-sense as time goes to infinity (Theorem 2.1).

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References

  1. S. Kawashima and M. Okada, On the equations of one-dimensional motion of compressible viscous fluids. J. Math. Kyoto. Univ.,23 (1983), 55–71.

    MATH  MathSciNet  Google Scholar 

  2. A.V. Kazhikhov and V.V. Shelukhin, Unique global solution with respect to time of the initial boundary value problems for one-dimensional equations of a viscous gas. J. Appl. Math. Mech.,41 (1977), 273–282.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Matsumura and T. Nishida, Initial boundary value problems for the equations of motion of compressible viscous fluids. Contemporary Mathmatics, Vol. 17, Nonlinear Partial Differential equations, Amer. Math. Soc., 1983.

  4. T. Nagasawa, On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary. J. Differential Equations,65 (1986), 49–67.

    Article  MATH  MathSciNet  Google Scholar 

  5. T. Nagasawa, On the outer pressure problem of the one-dimensional polytropic ideal gas. Japan J. Appl. Math.,5 (1988), 53–85.

    Article  MATH  MathSciNet  Google Scholar 

  6. T. Nishida, Equations of motion of compressible viscous fluids. Patterns and Waves—Qualitative Analysis of Nonlinear Differential Equations, Kinokuniya-North Holland, Tokyo-Amsterdam, 1986, 97–128.

    Book  Google Scholar 

  7. M. Okada, Free boundary value problem for equations of one-dimensional motion of compressible viscous fluids. Japan J. Appl. Math.,4 (1987), 219–235.

    MATH  MathSciNet  Google Scholar 

  8. M. Padula, Existence and continuous dependence for solutions to the equations of a one-dimensional model in gas dynamics. Mecanica, September, 1981, 128–135.

  9. J. Smoller, Shock Waves and Reaction-Diffusion Equations. Lecture Notes in Math.,258, Springer-Verlag, 1983.

  10. A. Tani, On the free boundary value problem for compressible viscous fluid motion. J. Math. Kyoto Univ.,21 (1981), 839–859.

    MATH  MathSciNet  Google Scholar 

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Author notes

  1. Sadamu Inaishi

    Present address: Guidance Laboratory, 3rd Research Center, Japan Defense Agency, Tachikawa, Japan

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Tokyo, 113, Tokyo, Japan

    Sadamu Inaishi

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  1. Sadamu Inaishi
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Inaishi, S. Free boundary value problem of the one-dimensional model of polytropic ideal gas. Japan J. Indust. Appl. Math. 8, 19–39 (1991). https://doi.org/10.1007/BF03167184

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  • DOI: https://doi.org/10.1007/BF03167184

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