This article is cited in 3 papers

Differential Equations

On one non-local problem for axisymmetric Helmholtz equation

A. A. Abashkin

Dept. of High Mathematics, Samara State Academy of Architecture and Construction, Samara

Abstract: Non-local boundary problem for the axisymmetric Helmholtz equation is explored. The uniqueness of the solution is proved by the spectral method. The conditions of solvability are found. The solution of the problem is constructed in the form of the biorthogonal series.

Keywords: Helmholtz equation, Bessel functions, non-local boundary problem, Riesz basis.

UDC: 517.956

MSC: Primary 35J05; Secondary 35J25, 35B30

Original article submitted 01/XII/2010
revision submitted – 15/VIII/2011

DOI: 10.14498/vsgtu852

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