Skip to main content

A Problem with Local and Nonlocal Conditions on the Boundary of the Ellipticity Domain for a Mixed Type Equation


For the Gellerstedt equation with a singular coefficient in some mixed domain, when the ellipticity boundary coincides with the segment of the Oy axis and the normal curve of the equation, a problem with the Bitsadze–Samarskii conditions on the elliptic boundary and on the degeneration line is studied. The well-posedness of the formulated problem is proved.

This is a preview of subscription content, access via your institution.


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

    Google Scholar 

  2. Salkhitdinov M.S., Mirsaburov M. Nonlocal Problems for Equations of Mixed Type with Singular Coefficients (Universitet, Tashkent, 2005) [in Russian].

    Google Scholar 

  3. Bitsadze A.V. Some Classes of Equations in Partial Derivatives (Nauka, Moscow, 1981) [in Russian].

    Google Scholar 

  4. Mirsaburov M., Khurramov N. "A problem with the Bitsadze–Samarskii condition on the characteristics of one family and with general transmission conditions on the degeneration line for the Gellerstedt equation with a singular coefficient", Differ. Equ. 56 (8), 1050-1071 (2020).

    MathSciNet  Article  Google Scholar 

  5. Mikhlin S.G. "On the F. Tricomi integral equation", Sov. Phys. Dokl. 59 (6), 1053-1056 (1948) [in Russian].

    Google Scholar 

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

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding authors

Correspondence to M. Mirsaburov or N. Kh. Khurramov.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 80–93.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mirsaburov, M., Khurramov, N.K. A Problem with Local and Nonlocal Conditions on the Boundary of the Ellipticity Domain for a Mixed Type Equation. Russ Math. 65, 68–81 (2021).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • extremum principle
  • uniqueness of a solution
  • Tricomi singular integral equation
  • existence of a solution
  • kernel with a first-order singularity at an isolated singular point
  • Wiener–Hopf equation
  • index