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 

Smol'kin Evgeniy Yur'evich, Candidate of physical and mathematical sciences, associate professor, sub-department of mathematics and supercomputer modeling, Penza State University (40, Krasnaya street, Penza, Russia), E-mail: e.g.smolkin@hotmail.com
Snegur Maksim Olegovich, Postgraduate student, Penza State University (40, Krasnaya street, Penza, Russia), E-mail: snegur.max15@gmail.com
Lapich Andrey Olegovich, Student, Penza State University (40, Krasnaya street, Penza, Russia), E-mail: lapich.a@yandex.ru
Gamayunova Lyudmila Yur'evna, Student, Penza State University (40, Krasnaya street, Penza, Russia), E-mail: gamayunova.mila@yandex.ru 

517.927.2:621.372.8 

10.21685/2072-3040-2019-3-3 

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. 

electromagnetic wave propagation problem, shielded (closed) dielectric waveguide with circular cross section, Maxwell equation, differential equations, variational formulation, Sobolev spaces 

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