Bitsadze-Samarsky type problems with double involution
Muratbekova M. Karachik V. Turmetov B.
December 2024Springer Science and Business Media Deutschland GmbH
Boundary Value Problems
2024#2024Issue 1
In this paper, the solvability of a new class of nonlocal boundary value problems for the Poisson equation is studied. Nonlocal conditions are specified in the form of a connection between the values of the unknown function at different points of the boundary. In this case, the boundary operator is determined using matrices of involution-type mappings. Theorems on the existence and uniqueness of solutions to the studied problems are proved. Using Green’s functions of the classical Dirichlet and Neumann boundary value problems, Green’s functions of the studied problems are constructed and integral representations of solutions to these problems are obtained.
Dirichlet problem , Green’s function , Involution , Neumann problem , Nonlocal problem , Orthogonal matrix , Poisson equation
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Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, B.Sattarkhanov 29, Turkistan, Turkistan, 161200, Kazakhstan
Department of Mathematical Analysis, South Ural State University, 76, Lenin prospekt, Ural Federal District, Chelyabinsk, 454080, Russian Federation
Department of Mathematics
Department of Mathematical Analysis
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