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

Abstract

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.

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

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

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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). https://doi.org/10.3103/S1066369X21120070

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  • DOI: https://doi.org/10.3103/S1066369X21120070

Keywords

  • 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