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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, Volume 20, Number 4, Pages 589–602 (Mi vsgtu1501)

This article is cited in 1 scientific paper (total in 1 paper)

Differential Equations and Mathematical Physics

The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain

N. V. Zaitseva

Kazan (Volga Region) Federal University, Kazan, 420008, Russian Federation

Abstract: We consider a boundary value problem for a hyperbolic equation with Bessel differential operator in a rectangular domain with integral nonlocal boundary value condition of the first kind. The equivalence between boundary value problem with integral nonlocal condition of the first kind and a local boundary value problem with mixed boundary conditions of the first and third kinds is proved. The existence and uniqueness of solution of the equivalent problem are established by means of the spectral method. At the uniqueness proof the completeness of the eigenfunction system of the spectral problem is used . At the existence proof the assessment of coefficients of series, the asymptotic formula for Bessel function of the first kind and asymptotic formula for eigenvalues are used. Sufficient conditions on the functions defining initial data of the problem are received. The solution of the problem is obtained in explicit form. The solution is obtained in the form of the Fourier–Bessel series. Its convergence is proved in the class of regular solutions.

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

DOI: https://doi.org/10.14498/vsgtu1501

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Bibliographic databases:

UDC: 517.956.3
MSC: 35L20, 35L81
Original article submitted 12/VII/2016
revision submitted – 12/XII/2016

Citation: N. V. Zaitseva, “The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 20:4 (2016), 589–602

Citation in format AMSBIB
\Bibitem{Zai16} \by N.~V.~Zaitseva \paper The nonlocal problem for a~hyperbolic equation with Bessel operator in~a~rectangular domain \jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.] \yr 2016 \vol 20 \issue 4 \pages 589--602 \mathnet{http://mi.mathnet.ru/vsgtu1501} \crossref{https://doi.org/10.14498/vsgtu1501} \zmath{https://zbmath.org/?q=an:06964657} \elib{http://elibrary.ru/item.asp?id=28862956} 

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This publication is cited in the following articles:
1. K. B. Sabitov, N. V. Zaitseva, “Initial-boundary value problem for hyperbolic equation with singular coefficient and integral condition of second kind”, Lobachevskii Journal of Mathematics, 39:9 (2018), 1419–1427
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