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

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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 11 scientific papers (total in 11 papers)

The second initial-boundary value problem for a

B

$B$ -hyperbolic equation

K. B. Sabitov^ab, N. V. Zaitseva^c

^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 (11)

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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

$B$ -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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Linking options:

https://www.mathnet.ru/eng/ivm9508

https://www.mathnet.ru/eng/ivm/y2019/i10/p75

This publication is cited in the following 11 articles:

A. V. Glushak, “On the Unique Solvability of Nonlocal Problems for Abstract Singular Equations”, Math. Notes, 115:5 (2024), 706–718
Yu. N. Bulatov, “Commutators of singular $\varvec{\mathbb {K}}$ -pseudodifferential operators in $\varvec{\mathbb {R}_n}$ ”, J. Pseudo-Differ. Oper. Appl., 15:4 (2024)
Yu. N. Bulatov, “Gording's Inequality for Singular J-Pseudodifferential Kipriyanov Operators”, Lobachevskii J Math, 45:11 (2024), 5458
L. N. Lyakhov, Yu. N. Bulatov, S.A. Roschupkin, E. L. Sanina, “Fundamentalnoe reshenie singulyarnogo differentsialnogo operatora Besselya s otritsatelnym parametrom”, Izv. vuzov. Matem., 2023, no. 7, 52–65
N. V. Zaitseva, “Mixed Problems with Integral Conditions for Hyperbolic Equations with the Bessel Operator”, Diff Equat, 59:S1 (2023), 1
L. N. Lyakhov, E. L. Sanina, S. A. Roshchupkin, Yu. N. Bulatov, “Fundamental Solution of a Singular Bessel Differential Operator with a Negative Parameter”, Russ Math., 67:7 (2023), 43
A. V. Glushak, “Uniqueness Criterion for Solutions of Nonlocal Problems on a Finite Interval for Abstract Singular Equations”, Math. Notes, 111:1 (2022), 20–32
L. N. Lyakhov, Yu. N. Bulatov, S. A. Roshchupkin, E. L. Sanina, “Pseudoshift and the Fundamental Solution of the Kipriyanov $\Delta _B$ -Operator”, Diff Equat, 58:12 (2022), 1639
Zh. A. Balkizov, “Zadacha so smescheniem dlya vyrozhdayuschegosya giperbolicheskogo uravneniya pervogo roda”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 25:1 (2021), 21–34
A. I. Kozhanov, “Nachalno-granichnye zadachi dlya vyrozhdayuschikhsya giperbolicheskikh uravnenii”, Sib. elektron. matem. izv., 18:1 (2021), 43–53
L. N. Lyakhov, K. S. Yeletskikh, E. L. Sanina, “Boundary value problems for the Euler-Poisson-Darboux equation”, Lobachevskii J. Math., 41:5, SI (2020), 797–809

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Известия высших учебных заведений. Математика

Russian Mathematics (Izvestiya VUZ. Matematika)

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