This article is cited in 15 papers

The second initial-boundary value problem for a $B$-hyperbolic equation

K. B. Sabitov^ab, N. V. Zaitseva<sup>c

a</sup> Sterlitamak branch of Bashkir State University, 37 Lenin Ave., Sterlitamak, 453103 Russia
^b Institute of Strategic Studies of Bashkortostan Republic, 68 Odesskaya str., Sterlitamak, 453103 Russia
^c Kazan Federal University, 35 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We investigate an initial-boundary value problem in a rectangular domain for a hyperbolic equation with Bessel operator. The solution is obtained in the form of the Fourier–Bessel series. The uniqueness of solution of the problem is established by means of the method of integral identities. At the existence of the proof we use assessment of coefficients of series, the asymptotic formula for Bessel function and asymptotic formula for eigenvalues. We obtain sufficient conditions on the functions defining initial data of the problem and prove the stability theorem for the solution of the problem.

Keywords: hyperbolic equation, Bessel differential operator, initial-boundary value problem, uniqueness, existence, Fourier–Bessel series, uniform convergence, stability.

UDC: 517.95

Received: 02.09.2018
Revised: 02.09.2018
Accepted: 19.12.2018

DOI: 10.26907/0021-3446-2019-10-75-86

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:10, 66–76

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