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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 10, Pages 75–86
DOI: https://doi.org/10.26907/0021-3446-2019-10-75-86 (Mi ivm9508) 		 
This article is cited in 9 scientific papers (total in 9 papers)

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

K. B. Sabitovab, N. V. Zaitsevac

a 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
Full-text PDF (406 kB) Citations (9)
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DOI: https://doi.org/10.26907/0021-3446-2019-10-75-86
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.
Funding agency Grant number
Kazan' Federal University 0212/02.12.10179.001
Received: 02.09.2018
Revised: 02.09.2018
Accepted: 19.12.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 10, Pages 66–76
DOI: https://doi.org/10.3103/S1066369X19100086
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: K. B. Sabitov, N. V. Zaitseva, “The second initial-boundary value problem for a $B$-hyperbolic equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 10, 75–86; Russian Math. (Iz. VUZ), 63:10 (2019), 66–76
Citation in format AMSBIB
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\paper The second initial-boundary value problem for a $B$-hyperbolic equation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\issue 10
\pages 75--86
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\crossref{https://doi.org/10.26907/0021-3446-2019-10-75-86}
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\issue 10
\pages 66--76
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    • This publication is cited in the following 9 articles:
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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