Gani A. Besbaev, Isabek Orazov, Makhmud A. Sadybekov
Abstract:
In the present work we investigate the nonlocal boundary problem for
the Laplace equation in a half disk. The difference of this problem
is the impossibility of direct applying of the Fourier method
(separation of variables). Because the corresponding spectral problem
for the ordinary differential equation has the system of eigenfunctions
not forming a basis. Based on these eigenfunctions there is constructed
a special system of functions that already forms the basis.
This is used for solving of the nonlocal boundary equation. The existence
and the uniqueness of the classical solution of the problem are proved.
Submitted July 11, 2014. Published September 30, 2014.
Math Subject Classifications: 33C10, 34B30, 35P10.
Key Words: Laplace equation; basis; eigenfunctions;
nonlocal boundary value problem.
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Gani A. Besbaev Faculty of Information technology Auezov South Kazakhstan state University Shymkent, Kazakhstan email: besbaev@mail.ru |
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Isabek Orazov The Natural-Pedagogical faculty Auezov South Kazakhstan state University Shymkent, Kazakhstan email: i_orazov@mail.ru |
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Makhmud A. Sadybekov Institute of Mathematics and Mathematical Modeling Almaty, Kazakhstan email: makhmud-s@mail.ru |
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