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Russian Mathematics

, Volume 63, Issue 10, pp 1–12 | Cite as

Dirichlet Problem in Parallelepiped for Elliptic Equation with Three Singular Coefficients

  • A. A. AbashkinEmail author
  • I. P. EgorovaEmail author
Article
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Abstract

We study the Dirichlet problem in the parallelepiped for an equation that is an analogue of the generalized bi-axisymmetric Helmholtz equation for the case of three independent variables. Using spectral analysis methods, we prove the uniqueness of the solution to the problem under study. The solution is constructed in the form of a double series using expansion in a Fourier-Bessel series. Sufficient conditions for the initial data of the problem are found under which the corresponding series converge uniformly and a solution exists.

Key words

equation with singular coefficients Dirichlet problem spectral method Bessel function double series 

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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Samara State Technical UniversitySamaraRussia

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