Skip to main content
SpringerLink
Log in

A nonlocal problem for a mixed-type equation with a singular coefficient in an unbounded domain

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

In this paper we study a nonlocal problem for a mixed-type equation in a domain whose elliptic part is the first quadrant of the plane and the hyperbolic part is the characteristic triangle. With the help of the method of integral equations and the principle of extremum we prove the unique solvability of the considered problem.

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. G. D. Sevost’yanov, “The Tricomi Boundary-Value Problem for a Half-Strip and a Quarter of a Plane,” Volzhsk.Matem. Sborn., No. 3, 312–320 (1965).

  2. S. Gellerstedt, “Quelques Problèmes Mixtes Pour l’Équation y m z xx + z yy = 0,” Ark. Mat. Astron. Fysik. 26A(3), 1–32 (1938).

    Google Scholar 

  3. A. V. Bitsadze, “On a Frankl’s Problem,” Sov. Phys. Dokl. 109(6), 1091–1094 (1956).

    MATH  MathSciNet  Google Scholar 

  4. Yu. V. Devingtal’, “The Existence and Uniqueness of the Solution of a Problem of F. I. Frankl,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 2, 39–51 (1958).

  5. N.M. Flaisher, “On a Problemof Frankl’ for the Lavrent’ev Equation in the Case of an Unbounded Region,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 6, 152–156 (1966).

  6. R. S. Khairullin, “Tricomi Problem for an Equation with Singular Coefficients,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 3, 68–76 (1996) [Russian Mathematics (Izv. VUZ) 40 (3), 66–74 (1996)].

  7. A. A. Polosin, “The Unique Solvability of the Tricomi Problem for a Special Domain,” Differents. Uravneniya 32(3), 394–401 (1996).

    MathSciNet  Google Scholar 

  8. V. I. Zhegalov, “A Boundary-Value Problem for an Equation of Mixed Type with Boundary Conditions on Both Characteristics and with Discontinuities on the Transition Curve,” Uchen. Zap. Kazansk. Univ. 122(3), 3–16 (1962).

    MATH  Google Scholar 

  9. M. Mirsaburov, “A Boundary-Value Problem for a Class of Mixed Equations with the Bitsadze-Samarskii Condition on Parallel Characteristics,” Differents. Uravneniya 37(9), 1281–1284 (2001).

    MathSciNet  Google Scholar 

  10. M. M. Smirnov, Equations of Mixed Type (Vyssh. Shkola, Moscow, 1985) [in Russian].

    Google Scholar 

  11. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications (Nauka i Tekhnika, Minsk, 1987; Gordon and Breach, New York, 1993).

    Google Scholar 

  12. M. S. Salakhitdinov and M. Mirsaburov, Nonlocal Problems for Equations of Mixed Type with Singular Coefficients (NUUz, Tashkent, 2005) [in Russian].

    Google Scholar 

  13. M. Kh. Ruziev, “The Tricomi Boundary-Value Problem for an Equation of Mixed Type with a Singular Coefficient in an Unbounded Domain,” Dokl. Akad. Nauk RUz, No. 6, 5–8 (2007).

  14. I. S. Gradshtein and I.M. Ryzhik, Tables of Integrals, Series, and Products (Nauka, Moscow, 1971; New York, Springer, 1971).

    Google Scholar 

  15. F. D. Gakhov and Yu. I. Cherskii, Equations of Convolution Type (Nauka, Moscow, 1978) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Information Technologies, Academy of Sciences of Republic of Uzbekistan, ul. Durman Iuli 29, Tashkent, 100125, Republic of Uzbekistan

    M. Kh. Ruziev

Authors
  1. M. Kh. Ruziev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Kh. Ruziev.

Additional information

Original Russian Text © M.Kh. Ruziev, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 11, pp. 41–50.

About this article

Cite this article

Ruziev, M.K. A nonlocal problem for a mixed-type equation with a singular coefficient in an unbounded domain. Russ Math. 54, 36–43 (2010). https://doi.org/10.3103/S1066369X10110046

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X10110046

Key words and phrases

Search

Navigation