Mathematics

On one problem in infinity strip for biaxisymmetric Helmholz equation

A. A. Abashkin

Dept. of Higher Mathematics, Samara State University of Architecture and Civil Engineering, Samara, 443001, Russian Federation

Abstract: Boundary value problem with special conditions on line $y=0$ in infinity strip 0<x<a for generalized biaxisymmetric Helmholz equation is set. Conditions of this problem set difference of some one-sided limits of known functions. Unknown function is zero in the right boundary and in infinity. Unknown functions with weight for one parameter $\mu$ value and without weight for other. Existence of solution is proved for some conditions. Uniqueness of solutions is proved for other some conditions.

Keywords: Helmholz equation, problem about leap, Bessel function, Fourie – Bessel series, maximal principle.

UDC: 517.956.6

Received: 22.05.2012
Revised: 22.05.2012