Skip to main content
SpringerLink
Log in

On a boundary-value problem for a functional-differential hyperbolic equation of the third order

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We consider a boundary-value problem for a functional-differential factorized hyperbolic equation of the third order not investigated earlier. We prove the existence and uniqueness of its solution.

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. Zhegalov, V. I., Mironov, A. N., and Utkina, E. A. Equations with Dominating Partial Derivative (Kazan Univ. Press, Kazan, 2014) [in Russian].

    MATH  Google Scholar 

  2. Zarubin, A. N. Mixed Type Equations with Delayed Argument. Manual (OGU, Orel, 1997) [in Russian].

    MATH  Google Scholar 

  3. Andreev, A. A. “Analogs of Classical Boundary Value Problems for a Second-Order Differential Equation with Deviating Argument”, Differ. Equ. 40, No. 8, 1192–1194 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  4. Utkina, E. A. “Characteristic Boundary-Value Problem for a Third-Order Equation with Pseudo-Parabolic Operator and with Shifted Arguments of Desired Function”, Russian Mathematics (Iz. VUZ) 58, No. 2, 45–50 (2014).

    MathSciNet  MATH  Google Scholar 

  5. Zhegalov, V. I. and Utkina, E. A. “Problems with Normal Derivatives in the Boundary Conditions for a Hyperbolic Equation with Deviating Arguments of the Unknown Function”, Differ. Equ. 50, No. 2, 226–231 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  6. Dzhuraev, T. D. and Popëlek, Ya. “Canonical Forms of Third-Order Partial Differential Equations”, Russian Math. Surveys 44, No. 4, 203–204 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  7. Elubaev, S. E. “A Boundary-value Problem for a Third-orderHyperbolic Equation”, Sibirsk.Mat. Z. 2, No. 4, 510–519 (1961) [in Russian].

    MathSciNet  Google Scholar 

  8. Elubaev, S. E. “On a Boundary Value Problem for a Hyperbolic Equation of the Third Order With Two Independent Variables”, Vestnik AN KazSSR, No. 6, 54–62 (1962) [in Russian].

    Google Scholar 

  9. Dzhuraev, T. D. “On Equations of Mixed Composed Type”, Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 6, 3–14 (1961) [in Russian].

    Google Scholar 

  10. Dzhuraev, T. D. “About Some Boundary Value Problems for Equations of Mixed-Composite Type”, Sib. Matem. Zhurn. 4, No. 4, 775–787 (1963) [in Russian].

    Google Scholar 

  11. Ni, Xingtang. “Boundary Value Problem with Three Characteristic Supports for Linear Totally Hyperbolic Equation of the Third Order”, Kexue Tongbao 25, No. 5, 361–369 (1980).

    MathSciNet  MATH  Google Scholar 

  12. Zhegalov, V. I. “About a Boundary Problem for Partial Differential Equations of the Third Order”, in Proceedings of International Conference on Spectral Theory of Differential Operators and Related Problems (Sterlitamak, 2003), Vol. 1, pp. 119–123.

    Google Scholar 

  13. Bitsadze, A. V. Equations of Mathematical Physics (Mir,Moscow, 1976) [in Russian].

    MATH  Google Scholar 

  14. Kolmogorov, A. N. and Fomin, S. V. Elements of Theory of Functions and Functional Analysis (Nauka, Moscow, 1976) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    E. A. Utkina

Authors
  1. E. A. Utkina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. A. Utkina.

Additional information

Original Russian Text © E.A. Utkina, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 8, pp. 69–73.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Utkina, E.A. On a boundary-value problem for a functional-differential hyperbolic equation of the third order. Russ Math. 60, 60–63 (2016). https://doi.org/10.3103/S1066369X16080077

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X16080077

Keywords

Search

Navigation