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University proceedings. Volga region. Physical and mathematical sciences, 2019, Issue 3, Pages 36–46
DOI: https://doi.org/10.21685/2072-3040-2019-3-3 (Mi ivpnz108) 		 
Mathematics

The study of nonlinear eigenvalue problems for the Maxwell equation system describing the propagation of electromagnetic waves in regular nonuniform shielded (closed) waveguide structures of circular cross section

E. Yu. Smol'kin, M. O. Snegur, A. O. Lapich, L. Yu. Gamayunova

Penza State University, Penza
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DOI: https://doi.org/10.21685/2072-3040-2019-3-3
Abstract: Background. The purpose of the work is to study the spectrum of the problem of propagating electromagnetic waves in regular inhomogeneous shielded (closed) waveguide structures of circular cross section. Material and methods. To find a solution, the method of operator pencils and operator functions is used. Results. The spectral properties of propagating (decaying) waves in regular inhomogeneous shielded (closed) waveguide structures are studied. Conclusions. The proposed approach can be generalized to study the wave spectrum of regular inhomogeneous shielded (closed) waveguide structures of arbitrary cross section.
Keywords: electromagnetic wave propagation problem, shielded (closed) dielectric waveguide with circular cross section, Maxwell equation, differential equations, variational formulation, Sobolev spaces.
Funding agency Grant number
Grant Council of the President of the Russian Federation МК- 242.2019.1
The work was written with the support of the Grants Council of the President of the Russian Federation for state support of young Russian scientists (grant of the President No. MK-242.2019.1).
Document Type: Article
UDC: 517.927.2:621.372.8
Language: Russian
Citation: E. Yu. Smol'kin, M. O. Snegur, A. O. Lapich, L. Yu. Gamayunova, “The study of nonlinear eigenvalue problems for the Maxwell equation system describing the propagation of electromagnetic waves in regular nonuniform shielded (closed) waveguide structures of circular cross section”, University proceedings. Volga region. Physical and mathematical sciences, 2019, no. 3, 36–46
Citation in format AMSBIB
\Bibitem{SmoSneLap19}
\by E.~Yu.~Smol'kin, M.~O.~Snegur, A.~O.~Lapich, L.~Yu.~Gamayunova
\paper The study of nonlinear eigenvalue problems for the Maxwell equation system describing the propagation of electromagnetic waves in regular nonuniform shielded (closed) waveguide structures of circular cross section
\jour University proceedings. Volga region. Physical and mathematical sciences
\yr 2019
\issue 3
\pages 36--46
\mathnet{http://mi.mathnet.ru/ivpnz108}
\crossref{https://doi.org/10.21685/2072-3040-2019-3-3}
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