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Differential Equations

, Volume 55, Issue 10, pp 1384–1389 | Cite as

Dezin Problem for an Equation of the Mixed Type with a Power-Law Degeneracy

  • K. B. SabitovEmail author
Partial Differential Equations
  • 6 Downloads

Abstract

We study a boundary value problem with periodicity conditions and with a nonlocal Dezin condition for a mixed elliptic-hyperbolic equation in a rectangular domain with power-law degeneracy on the transition line. Necessary and sufficient conditions for the uniqueness of the solution are established, the uniqueness of the solution being proved based on the completeness of the system of eigenfunctions of a one-dimensional eigenvalue problem. The solution is constructed in the form of a series. The problem of small denominators occurs when justifying the convergence of the series. Under some conditions imposed on the given parameters and functions, the convergence of the series is proved in the class of regular solutions.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Sterlitamak BranchInstitute for Strategic Studies, BashkortostanSterlitamakRussia
  2. 2.Sterlitamak BranchBashkir State University, BashkortostanSterlitamakRussia

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