M. Mirsaburov, N. Kh. Khurramov, “A problem with local and nonlocal conditions on the boundary of the ellipticity domain for a mixed type equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, Number 12,Pages <nobr>80

A problem with local and nonlocal conditions on the boundary of the ellipticity domain for a mixed type equation

M. Mirsaburov, N. Kh. Khurramov

Termez State University, 43 Barkamol avlod str., Termez, 190111 Republic of Uzbekistan

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, the problem with the Bitsadze–Samarskii conditions on the elliptic boundary and on the degeneration line is studied. The correctness of the formulated problem is proved.

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

UDC: 517.956

Received: 22.02.2021
Revised: 22.02.2021
Accepted: 29.06.2021

DOI: 10.26907/0021-3446-2021-12-80-93