On Some Problems of Bitsadze–Samarsky Type for the Poisson Equation
Turmetov B.K. Nazarova K.Z. Usmanov K.I.
July 2024Pleiades Publishing
Lobachevskii Journal of Mathematics
2024#45Issue 73444 - 3452 pp.
Abstract: The paper is devoted to the study of the solvability of some nonlocal boundary value problems for the Poisson equation in the unit ball. 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. An explicit form of the Green’s function and an integral representation of solutions to the studied problems are constructed.
Bitsadze–Samarsky problem , existence and uniqueness , Green’s function , involution , nonlocal problem , Poisson’s equation
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Yasawi International Kazakh–Turkish University, Turkistan, 161200, Kazakhstan
Yasawi International Kazakh–Turkish University
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