Dirichlet problem in parallelepiped for elliptic equation with three singular coefficients

A. A. Abashkin, I. P. Egorova

Samara State Technical University, 244 Molodogvardeyskaya str., Samara, 443100, Russia

Abstract: For analog Helmholz biaxisymmetric equation for the case of three variable, we consider Dirichlet problem in parallelepiped. We prove uniqueness of Dirichlet problem solution using spectral analysis methods. We construct the Dirichlet problem solution as double series. In constructing the solutions we use Fourier–Bessel series. We find boundary function the conditions, then the corresponding series converges uniformly.

Keywords: equation with singular coefficients, Dirichlet problem, spectral method, Bessel functions, double row.

UDC: 517.956

Received: 29.08.2018
Revised: 29.08.2018
Accepted: 27.03.2019

DOI: 10.26907/0021-3446-2019-10-3-14

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:10, 1–12

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