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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2022 Volume 211, Pages 114–130 (Mi into1028)

This article is cited in 1 paper

Boussinesq integro-differential equation with integral conditions and a small coefficient of mixed derivatives

T. K. Yuldasheva, F. D. Rakhmonova, A. S. Ismoilovb

a National University of Uzbekistan named after M. Ulugbek, Tashkent
b Samarkand State University

Abstract: In this paper, we prove the unique solvability of a nonlocal boundary-value problem for a high-order, three-dimensional, linear Boussinesq integro-differential equation with a degenerate kernel and general integral conditions and construct a solution in the form of a Fourier series. The absolute and uniform convergence of the resulting series and the possibility of term-by-term differentiation of the solution with respect to all variables are established. A criterion for the unique solvability of the boundary-value problem in the case of regular values of the parameter is obtained. For irregular values of the parameter, an infinite set of solutions is constructed in the form of a Fourier series.

Keywords: integro-differential equation, Boussinesq equation, mixed derivative, unique solvability, integral condition, degenerate kernel.

UDC: 517.968.74

MSC: 35A02, 35M10, 35S05

DOI: 10.36535/0233-6723-2022-211-114-130



© Steklov Math. Inst. of RAS, 2025