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Solvability “in the large” of a system of equations of the one-dimensional motion of an inhomogeneous viscous heat-conducting gas

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Literature cited

  1. B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  2. S. N. Antontsev, A. V. Kazhikhov, and V. N. Monakhov, Boundary-Value Problems of the Mechanics of Inhomogeneous Fluids [in Russian], Nauka, Novosibirsk (1983).

    Google Scholar 

  3. A. V. Kazhikhov, “Sur la solubilité globale des problèmes monodimensionels aux valeurs initiales-limites pour les equations d'un gas visqueux et calorifère,” C. R. Acad. Sci. Paris, Sér. A,284, 317–320 (1977).

    Google Scholar 

  4. A. V. Kazhikov and V. V. Shelukhin, “The unique solvability in the large with respect to time of initial boundary-value problems for the one-dimensional equations of a viscous gas,” Prikl. Mat. Mekh.,41, 2, 282–291 (1977).

    Google Scholar 

  5. A. A. Amosov and A. A. Zlotnik, “Generalized solutions ‘in the large’ of the equations of the one-dimensional motion of a viscous heat-conducting gas,” Dokl. Akad. Nauk SSSR,301, No. 1, 11–15 (1988).

    Google Scholar 

  6. D. Serre, “Sur l'équation monodimensionelle d'un fluide visqueux compressible et conducteur de chaleur,” C. R. Acad. Sci. Paris, Sér. I,303, No. 14, 703–706 (1986).

    Google Scholar 

  7. V. V. Shelukhin, “Motion with a contact discontinuity in a viscous heat-conducting gas,” in: Dynamics of Continua [in Russian], Novosibirsk (1982), No. 57, pp. 131–152.

    Google Scholar 

  8. N. S. Bakhvalov and M. É. Églit, “Processes in periodic media not describable in terms of mean characteristics,” Dokl. Akad. Nauk SSSR,268, No. 4, 836–840 (1983).

    Google Scholar 

  9. O. A. Ladyzhenskaya, A. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  10. A. A. Amosov and A. A. Zlotnik, “A study of a finite-difference method for the one-dimensional viscous heat-conductive gas flow equations. Part I. A priori estimates and stability,” Sov. J. Numer. Anal. and Math. Model.,2, No. 3, 159–178 (1987).

    Google Scholar 

  11. O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and the Theory of Imbedding [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  12. S. M. Nikol'skii, The Approximation of Functions of Many Variables and Theorems of Imbedding [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  13. A. V. Kazhikhov, “A priori estimates of the solutions of the equations of magnetic gas dynamics,” in: Boundary-Value Equations of Mathematical Physics [in Russian], Krasnoyarsk (1987), pp. 84–94.

  14. J.-L. Lions, Certain Methods of Solving Nonlinear Boundary-Value Problems [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  15. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).

    Google Scholar 

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Authors and Affiliations

  1. Moscow Energy Institute, USSR

    A. A. Amosov & A. A. Zlotnik

  2. V. I. Lenin Moscow State Pedagogical Institute, USSR

    A. A. Amosov & A. A. Zlotnik

Authors
  1. A. A. Amosov
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  2. A. A. Zlotnik
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Translated from Matematicheskii Zametki, Vol. 52, No. 2, pp. 3–16, August, 1992.

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Amosov, A.A., Zlotnik, A.A. Solvability “in the large” of a system of equations of the one-dimensional motion of an inhomogeneous viscous heat-conducting gas. Math Notes 52, 753–763 (1992). https://doi.org/10.1007/BF01236769

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  • DOI: https://doi.org/10.1007/BF01236769

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