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Boundary value problem for a model differential equation with involution in a rectangular domain
V. N. Lesev, O. I. Bzheumikhova, A. O. Zheldasheva, N. Kh. Etuev Kabardino-Balkar State University, Nal'chik
Abstract:
In the present work, the solvability of a classical boundary value problem for a degenerate partial differential equation of
the second order with an involutive deviation of the argument of the form (-x) in a rectangular domain is first established and
studied. The existence and uniqueness theorems of the regular solution are proved for the studied problem. Some conditions on
the coefficients, when fulfilling which the problem has a singular solution, are set. The question of solvability of the problem
in the required class of functions by the method of separation of variables is reduced to the solvability of the corresponding
ordinary differential equation with involutive deviation of the argument, the solution of which is constructed by the method of
differentiation.
Keywords:
equation with involution, singularity, existence, boundary value problem, differentiation method
Received: 06.09.2023 Revised: 17.11.2023 Accepted: 08.11.2023
Citation:
V. N. Lesev, O. I. Bzheumikhova, A. O. Zheldasheva, N. Kh. Etuev, “Boundary value problem for a model differential equation with involution in a rectangular domain”, Meždunar. nauč.-issled. žurn., 2023, no. 11(137), 1–7
Linking options:
https://www.mathnet.ru/eng/irj666 https://www.mathnet.ru/eng/irj/v137/i11/p1
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Abstract page: | 37 | Full-text PDF : | 52 | References: | 6 |
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