Email this article Initial-Boundary Value Problem for Hyperbolic Equation with Singular Coefficient and Integral Condition of Second Kind
- Authors: Sabitov K.B.1, Zaitseva N.V.2
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Affiliations:
- Sterlitamak Branch of the Bashkir State University
- N. I. Lobachevskii Institute of Mathematics and Mechanics
- Issue: Vol 39, No 9 (2018)
- Pages: 1419-1427
- Section: Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
- URL: https://journals.rcsi.science/1995-0802/article/view/203505
- DOI: https://doi.org/10.1134/S1995080218090299
- ID: 203505
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Abstract
We research an initial-boundary value problem with integral condition of the second kind in a rectangular domain for a hyperbolic equation with singular coefficient. The solution is obtained in the form of the Fourier–Bessel series. There are proved theorems on uniqueness, existence and stability of the solution. In order to prove the existence of solution of the non-local problem we obtain sufficient conditions for the convergence of the series in terms of the initial values.
About the authors
K. B. Sabitov
Sterlitamak Branch of the Bashkir State University
Author for correspondence.
Email: sabitov_fmf@mail.ru
Russian Federation, pr. Lenina 49, Sterlitamak, Bashkortostan, 453103
N. V. Zaitseva
N. I. Lobachevskii Institute of Mathematics and Mechanics
Email: sabitov_fmf@mail.ru
Russian Federation, ul. Kremlevskaya 18, Kazan, Tatarstan, 420008
