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MATHEMATICS

The keldysh problem for a mixed-type three-dimensional equation with three singular coefficients

K. T. Karimov

Fergana State University

Abstract: In this article, we study the Keldysh problem for a three-dimensional mixed-type equation with three singular coefficients in a rectangular parallelepiped. Based on the completeness property of systems of eigenfunctions of two one-dimensional spectral problems, a uniqueness theorem is proved. The solution to the problem posed is constructed as the sum of a double Fourier-Bessel series.

Keywords: Keldysh problem, mixed type equation, spectral method, singular coefficient, Bessel function.

UDC: 517.956.6

MSC: 35M12

DOI: 10.26117/2079-6641-2021-34-1-29-46