Skip to main content
SpringerLink
Log in

On stability of generalized solutions to the equations of one-dimensional motion of a viscous heat conducting gas

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

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

    Google Scholar 

  2. V. V. Shelukhin, “Motion with a contact discontinuity in a viscous heat conducting gas,” Dinamika Sploshn. Sredy (Novosibirsk), No. 57, 131–152 (1982).

    Google Scholar 

  3. D. Serre, “Sur l'équation monodimensionnelle d'un fluide visqueux, compressible et conducteur de chaleur,” C. R. Acad. Sci. Paris Sér. 1 Math.,303, No. 14, 703–706 (1986).

    MATH  Google Scholar 

  4. A. A. Amosov and A. A. Zlotnik, “Global generalized solutions to the equations of one-dimensional motion of a viscous heat conducting gas,” Dokl. Akad. Nauk SSSR,301, No. 1, 11–15 (1988).

    Google Scholar 

  5. A. A. Amosov and A. A. Zlotnik, “Global solvability of the system of equations of one-dimensional motion of an inhomogeneous viscous heat conducting gas,” Mat. Zametki,52, No. 2, 3–16 (1992).

    Google Scholar 

  6. H. Fujita-Yashima, M. Padula, and A. Novotný, “Equation monodimensionnelle d'un gas visqueux et calorifére avec des conditions initiales moins restrictives,” Ricerche Mat.,42, No. 2, 199–248 (1993).

    MATH  Google Scholar 

  7. D. Hoff, Discontinuous Solutions of the Navier-Stokes Equations for Multidimension Heat-Conducting Flow [Preprint/Indiana University; No. 9517], Indiana (1995).

  8. A. A. Amosov and A. A. Zlotnik, “A semidiscrete method for solving the equations of one-dimensional motion of an inhomogeneous viscous heat conducting gas with nonsmooth data,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 4, 3–19 (1997).

    Google Scholar 

  9. M. Padula, “Existence and continuous dependence for solutions to the equations of a one-dimensional model in gas-dynamics,” Meccanica J. AIMETA,16, No. 3, 128–135 (1981).

    Article  MATH  Google Scholar 

  10. A. A. Amosov and A. A. Zlotnik, “Global generalized solutions to the equations of one-dimensional motion of a viscous barotropic gas,” Dokl. Akad. Nauk SSSR,299, No. 6, 1303–1307 (1988).

    Google Scholar 

  11. A. A. Amosov and A. A. Zlotnik, “Uniqueness and stability of generalized solutions for a class of quasilinear composite-type systems of equations,” Mat. Zametki,55, No. 6, 13–31 (1994).

    Google Scholar 

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

    Google Scholar 

  13. E. Tornatore and H. Fujita-Yashima, “Equazioni monodimensionali di un gas viscoso barotropico con una perturbazione poco regolare,” Ann. Univ. Ferrara Sez. VII (N.S.),40, 137–168 (1994).

    Google Scholar 

  14. E. Tornatore and H. Fujita-Yashima, Equazione Stocastica Monodimensionale di un Gas Viscoso Barotropico [Preprint/Universitá degli Studi di Palermo; No. 19], Palermo (1996).

  15. A. A. Amosov and A. A. Zlotnik, “On properties of generalized solutions to one-dimensional linear parabolic problems with nonsmooth data,” Differentsial'nye Uravneniya,33, No. 1, 83–95 (1997).

    MATH  Google Scholar 

  16. A. A. Zlotnik, “The selection principle for functions of bounded variation with values in a Banach space,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 3, 52–55 (1979).

    Google Scholar 

  17. A. A. Amosov and A. A. Zlotnik, “Remarks on properties of generalized solutions inV 2(Q) to one-dimensional linear parabolic problems,” Vestnik MÈI, No. 6, 15–29 (1996).

    Google Scholar 

  18. O. V. Besov, V. P. Il'in, and C. M. Nikol'skiî, Integral Representations and Embedding Theorems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  19. M. Escobedo and E. Zuazua, “Large time behavior of convection-diffusion equations in {ie684-1},” J. Funct. Anal.,100, No. 1, 119–161 (1991).

    Article  MATH  Google Scholar 

  20. O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  21. S. N. Kruzhkov, “Quasilinear parabolic equations and systems in two independent variables,” Trudy Sem. Petrovsk., No. 5, 217–272 (1979).

    MATH  Google Scholar 

  22. A. A. Amosov and A. A. Zlotnik, “On quasi-averaged equations of one-dimensional motion of a viscous barotropic medium with rapidly oscillating data,” Zh. Vychisl. Mat. i Mat. Fiz.,36, No. 2, 87–110 (1996).

    Google Scholar 

  23. J. Bergh and J. Löfström, Interpolation Spaces. Introduction [Russian translation], Mir, Moscow (1980).

    Google Scholar 

Download references

Authors
  1. A. A. Zlotnik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Amosov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research was financially supported by the Russian Foundation for Basic Research (Grant 97-01-00214).

Moscow. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 4, pp. 767–789, July–August, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zlotnik, A.A., Amosov, A.A. On stability of generalized solutions to the equations of one-dimensional motion of a viscous heat conducting gas. Sib Math J 38, 663–684 (1997). https://doi.org/10.1007/BF02674573

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02674573

Keywords

Search

Navigation