Geodesic
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 Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3-4 (2016), pp. 51-62

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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
Mots-clés : existence. 
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     author = {N. V. Zaitseva},
     title = {The boundary value problem for a hyperbolic equation with {Bessel} operator in a rectangular domain with integral boundary value condition of the first kind},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {51--62},
     publisher = {mathdoc},
     number = {3-4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2016_3-4_a4/}
}
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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 Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3-4 (2016), pp. 51-62. http://geodesic.mathdoc.fr/item/VSGU_2016_3-4_a4/