Abstract:
In this article, we study a nonlocal problem for a fourth-order equation in which the existence and uniqueness of a solution to this problem is proved. The solution is constructed explicitly in the form of a Fourier series; the absolute and uniform convergence of the obtained series and the possibility of term-by-term differentiation of the solution with respect to all variables are substantiated. A criterion for the unique solvability of the stated boundary value problem is established.
Keywords:
boundary value problem, Fourier method, existence and uniqueness of the solution.
Citation:
O. Sh. Kilichov, “On a nonlocal boundary value problem for the equation fourth-order in partial derivatives”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 37:4 (2021), 16–23
\Bibitem{Kil21}
\by O.~Sh.~Kilichov
\paper On a nonlocal boundary value problem for the equation fourth-order in partial derivatives
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2021
\vol 37
\issue 4
\pages 16--23
\mathnet{http://mi.mathnet.ru/vkam504}
\crossref{https://doi.org/10.26117/2079-6641-2021-37-4-16-23}
Linking options:
https://www.mathnet.ru/eng/vkam504
https://www.mathnet.ru/eng/vkam/v37/i4/p16
This publication is cited in the following 1 articles:
O. Sh. Kilichov, A. N. Ubaydullaev, “Ob odnoi kraevoi zadache dlya uravneniya chetvertogo poryadka v chastnykh proizvodnykh”, Vestnik KRAUNTs. Fiz.-mat. nauki, 39:2 (2022), 32–41
Citation in format AMSBIB
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