Skip to main content
SpringerLink
Log in

On the outer pressure problem of the one-dimensional polytropic ideal gas

  • Published:
Japan Journal of Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper the existence of the global solution of the outer pressure problem of the one-dimensional polytropic ideal gas is proved (Theorem 1). We shall also investigate, under some suitable assumptions, the convergence of the solution to a stationary state (Theorem 2), and the rate of its convergene (Theorem 3).

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

Similar content being viewed by others

References

  1. S. Kawashima and T. Nishida, Global solutions to the initial value problem for the equations of one-dimensional motion of viscous polytropic gases. J. Math. Kyoto Univ.,21 (1981), 825–837.

    MATH  MathSciNet  Google Scholar 

  2. A. V. Kazhykhov (Kazhikhov), Sur la solubilité globale des problèmes monodimensionnels aux valeurs initiales-limitées pour les équations d’un gaz visqueux et calorifère. C. R. Acad. Sci. Paris Sér. A,284, (1977), 317–320.

    MathSciNet  Google Scholar 

  3. A. V. Kazhikhov, To the theory of boundary value problems for equations of a one-dimensional non-stationary motion of a viscous heat-conductive gas. Boundary Value Problems for Equations of Hydrodynamics. Institute of Hydrodynamics, Novosibirsk,50, (1981), 37–62 (Russian).

    Google Scholar 

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

    MathSciNet  Google Scholar 

  5. O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and Quasi-linear Equations of Parabolic Type. Transl. Math. Monographs.23, Amer. Math. Soc., Providence, R. I., 1968.

    Google Scholar 

  6. 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 

  7. M. H. Protter and H. F. Weinberger, Maximum Principle in Differential Equations. Springer-Verlag, New York, N.Y., 1984 (Originally published: Prentice Hall, Englewood Cliffs, N.J., 1967).

    Google Scholar 

  8. P. Secchi and A. Valli, A free boundary problem for compressible viscous fluids. J. Reine Angew. Math.,341, (1983), 1–31.

    MathSciNet  Google Scholar 

  9. 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 

  10. A. Tani. Free boundary problems for the equations of motion of general fluids. Lecture Note on Num. Appl. Anal.,6, (1983), 211–219.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Keio University, 223, Yokohama, Japan

    Takeyuki Nagasawa

Authors
  1. Takeyuki Nagasawa
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Nagasawa, T. On the outer pressure problem of the one-dimensional polytropic ideal gas. Japan J. Appl. Math. 5, 53–85 (1988). https://doi.org/10.1007/BF03167901

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03167901

Key words

Search

Navigation