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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, Issue 3-4, Pages 51–62 (Mi vsgu510)

Mathematics

The boundary value problem for a hyperbolic equation with Bessel operator in a rectangular domain with integral boundary value condition of the first kind

N. V. Zaitseva

Lobachevskii Institute of mathematics and mechanics, Kazan (Volga region) Federal University, Kazan, 420008, Russian Federation

Abstract: We consider a boundary value problem with integral nonlocal boundary condition of the first kind for a hyperbolic equation with Bessel differential operator in a rectangular domain.
The equivalence of this problem and a local problem with boundary conditions of the second kind is established.
The existence and uniqueness of solution of the equivalent problem are proved by means of the spectral method. The solution of the problem is obtained in the form of the Fourier–Bessel series. Convergence is proved in the class of regular solutions.

Keywords: hyperbolic equation, Bessel differential operator, non-local boundary value condition, Fourier–Bessel series, uniqueness, existence.

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UDC: 517.95

Citation: N. V. Zaitseva, “The boundary value problem for a hyperbolic equation with Bessel operator in a rectangular domain with integral boundary value condition of the first kind”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2016, no. 3-4, 51–62

Citation in format AMSBIB
\Bibitem{Zai16} \by N.~V.~Zaitseva \paper The boundary value problem for a hyperbolic equation with Bessel operator in a rectangular domain with integral boundary value condition of the first kind \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2016 \issue 3-4 \pages 51--62 \mathnet{http://mi.mathnet.ru/vsgu510} \elib{http://elibrary.ru/item.asp?id=29389325}