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Differential Equations

, Volume 54, Issue 1, pp 121–133 | Cite as

Initial Value Problem for B-Hyperbolic Equation with Integral Condition of the Second Kind

  • K. B. Sabitov
  • N. V. Zaitseva
Partial Differential Equations

Abstract

For the hyperbolic equation with Bessel operator, we study the initial boundaryvalue problem with integral nonlocal condition of the second kind in a rectangular domain. The integral identity method is used to prove the uniqueness of the solution to the posed problem. The solution is constructed as a Fourier–Bessel series. To justify the existence of the solution to the nonlocal problem, we obtain sufficient conditions to be imposed on the initial conditions to ensure the convergence of the constructed series in the class of regular solutions.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Bashkortostan Institute for Strategic ResearchSterlitamak, BashkortostanRussia
  2. 2.Sterlitamak Branch of Bashkir State UniversitySterlitamak, BashkortostanRussia
  3. 3.Kazan (Volga) Federal UniversityKazan, TatarstanRussia

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