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Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1419–1427 | Cite as

Initial-Boundary Value Problem for Hyperbolic Equation with Singular Coefficient and Integral Condition of Second Kind

  • K. B. SabitovEmail author
  • N. V. Zaitseva
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
  • 4 Downloads

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.

Keywords and phrases

hyperbolic equation singular coefficient non-local integral condition uniqueness Fourier–Bessel series existence stability 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Sterlitamak Branch of the Bashkir State UniversitySterlitamak, BashkortostanRussia
  2. 2.N. I. Lobachevskii Institute of Mathematics and MechanicsKazan (Volga Region) Federal UniversityKazan, TatarstanRussia

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