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This article is cited in 1 scientific paper (total in 1 paper)
Nonlocal problem for a three-dimensional elliptic equation with singular coefficients in a rectangular parallelepiped
Kamoliddin T. Karimov Ferghana State University, Ferghana, Uzbekistan
Abstract:
The nonlocal problem for an elliptic equation with two singular coefficients in a rectangular parallelepiped is studied. The uniqueness of the solution of the problem is proved with the use of the method of energy integrals. The spectral Fourier method based on the separation of variables is used to prove the existence of solutions. The solution of the problem is constructed as double Fourier series in terms of a sum of trigonometric and Bessel functions. Under some conditions on parameters and given functions the uniform convergence of the constructed series and its derivatives up to the second order inclusive is proved.
Keywords:
elliptic type equation, nonlocal problem, singular coefficient, spectral method, parallelepiped.
Received: 20.05.2020 Received in revised form: 14.06.2020 Accepted: 08.07.2020
Citation:
Kamoliddin T. Karimov, “Nonlocal problem for a three-dimensional elliptic equation with singular coefficients in a rectangular parallelepiped”, J. Sib. Fed. Univ. Math. Phys., 13:5 (2020), 533–546
Linking options:
https://www.mathnet.ru/eng/jsfu860 https://www.mathnet.ru/eng/jsfu/v13/i5/p533
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Abstract page: | 73 | Full-text PDF : | 37 | References: | 14 |
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