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2019•Russian MathematicsRequires access

Hilbert Boundary-Value Problem With Two-Side Curling at Infinity Point of Different Orders

E. N. Khasanova, П. Л. Шабалин

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Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Mathematics, Bessel function, Helmholtz equation, Mathematical analysis, Curling, Boundary value problem, Infinity, Fourier series

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