Inverse problems of the theory of cylindrical dipole antennas in Sobolev spaces
https://doi.org/10.34680/2076-8052.2024.3(137).498-506
Abstract
The inverse problems of antenna theory have been studied, in which surface currents are determined according to a given radiation pattern. The determination of axial and azimuthal currents is based on the solution of operator equations with small parameters.
To determine azimuthal currents, an integral operator with a logarithmic feature in the core is used, which acts as the main operator. And a hypersingular integro-differential operator is used to determine axial currents. The use of these operators makes it possible to determine surface currents with the desired behavior at the boundary. The density of axial currents when approaching the boundary vanishes according to the root law, and the density of azimuthal currents tends to infinity.
The main operators of equations with a small parameter are continuous and continuously invertible in Sobolev spaces. Therefore, operator equations with a small parameter are equivalent to Fredholm equations of the second kind. An example of numerical calculation is considered.
About the Authors
S. I. Eminov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
A. V. Sochilin
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
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Review
For citations:
Eminov S.I., Sochilin A.V. Inverse problems of the theory of cylindrical dipole antennas in Sobolev spaces. Title in english. 2024;(3(137)):498-506. (In Russ.) https://doi.org/10.34680/2076-8052.2024.3(137).498-506
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