Combined problem with local and non-local conditions and with general conjugation conditions for the Gellerstedt equation with a singular coefficient

M. Mirsaburov, B. B. Amonov

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

Abstract: In the Tricomi problem, the value of the desired function is specified at all points of the boundary characteristic. In this paper, we study the correctness of the problem where part of the boundary characteristic is freed from the boundary condition and this missing Tricomi condition is replaced by a nonlocal condition with displacement on the internal characteristic and on the part of the boundary characteristic. On the degeneracy segment, a general conjugation condition is specified.

Keywords: missing Tricomi condition, condition with displacement on the internal characteristic and on the part of the boundary characteristic, extremum principle, uniqueness of the solution, existence of the solution.

UDC: 517.956

Received: 19.07.2024
Revised: 08.02.2025
Accepted: 26.03.2025

DOI: 10.26907/0021-3446-2025-12-71-93