Skip to main content
SpringerLink
Log in

Uniqueness of the solution of the dirichlet problem for an n-dimensional pseudoparabolic equation

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

In an n-dimensional domain formed by the characteristic planes of an equation of order 2n with a double higher partial derivative, we derive sufficient conditions for the uniqueness of the solution of the Dirichlet problem. These conditions are written out in terms of the coefficients of the equation, and the argument is based on the method of a priori estimates.

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. Ladyzhenskaya, O.A., Kraevye zadachi matematicheskoi fiziki (Boundary Value Problems of Mathematical Physics), Moscow: Nauka, 1973.

    Google Scholar 

  2. Vladimirov, V.S., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1976.

    Google Scholar 

  3. Berezanskii, Yu.M., On a Dirichlet Type Problem for the Equation of String Vibrations, Ukrain. Mat. Zh., 1960, vol. 12, no. 4, pp. 363–372.

    Article  MathSciNet  Google Scholar 

  4. Vakhaniya, N.N., A Boundary Value Problem for a Hyperbolic System Equivalent to the String Vibration Equation, Dokl. Akad. Nauk SSSR, 1957, vol. 116, no. 6, pp. 906–909.

    MathSciNet  MATH  Google Scholar 

  5. Vakhaniya, N.N., On the Dirichlet Problem for the Equation of String Vibrations, Soobshch. Akad. Nauk GruzSSR, 1958, vol. 21, no. 2, pp. 131–138.

    MATH  Google Scholar 

  6. Fokin, M.V., On the Dirichlet Problem for the String Equation, in Nekorrektnye kraevye zadachi dlya neklassicheskikh uravnenii matematicheskoi fiziki (Ill-Posed Boundary Value problems for Nonclassical Equations of Mathematical Physics), Novosibirsk, 1981, pp. 178–182.

  7. Abdul-Latif, A.I., Dirichlet, Neumann and Mixed Dirichlet-Neumann Value Problems for u xy = 0 in Rectangles, Proc. Roy. Soc. Edinburgh, 1978, ser. A, no. 82, pp. 107–110.

  8. Kiguradze, T., On the Correctness of Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations, Georgian Math. J., 1999, vol. 6, no. 5, pp. 447–470.

    Article  MathSciNet  MATH  Google Scholar 

  9. Kiguradze, T. and Lakshmikanthem, V., On the Dirichlet Problem for Fourth-Order Linear Hyperbolic Equation, Nonlinear Anal., 2002, vol. 49, no. 2, pp. 197–219.

    Article  MathSciNet  MATH  Google Scholar 

  10. Soldatov, A.P. and Shkhanukov, M.Kh., Boundary Value Problems with A. A. Samarskii’s General Nonlocal Condition for Higher-Order Pseudoparabolic Equations, Dokl. Akad. Nauk SSSR, 1987, vol. 297, no. 3, pp. 547–552.

    MathSciNet  Google Scholar 

  11. Utkina, E.A., The Dirichlet Problem for a Fourth-Order Equation, Differ. Uravn., 2011, vol. 47, no. 4, pp. 400–404.

    MathSciNet  Google Scholar 

  12. Utkina, E.A., A Uniqueness Theorem for the Solution of a Dirichlet Problem, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 5, pp. 62–67.

  13. Utkina, E.A., Dirichlet Problem for a Three-Dimensional Equation, Vestn. Samar. Gos. Univ. Estestvennonauch. Ser., 2010, vol. 2(76), pp. 84–95.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan Federal University, Kazan, Russia

    E. A. Utkina

Authors
  1. E. A. Utkina
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © E.A. Utkina, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 10, pp. 1443–1449.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Utkina, E.A. Uniqueness of the solution of the dirichlet problem for an n-dimensional pseudoparabolic equation. Diff Equat 48, 1423–1428 (2012). https://doi.org/10.1134/S0012266112100126

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266112100126

Keywords

Search

Navigation