This article is cited in 5 papers

On a weighted boundary value problem in an infinite half-strip for a biaxisymmetric Helmholtz equation

A. A. Abashkin

Chair of Higher Mathematics, Samara State University of Architecture and Civil Engineering, Samara, Russia

Abstract: We study a boundary value problem for a generalized biaxisymmetric Helmholtz equation. Boundary conditions in this problem depend on equation parameters. By the variable separation method, using the Fourier–Bessel series expansion and the Hankel transform, we prove the unique solvability of the problem and establish explicit formulas for the solution.

Keywords: Helmholz equation, Fourier–Bessel series, Hankel transformation, Bessel functions.

UDC: 517.956

Received: 28.03.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:6, 1–9

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