Abstract:
The paper deals with two problems of waveguide theory: the problem
of radiation of electromagnetic waves in a regular waveguide with a filling
variable in the cross-sections, and the problem of diffraction of an
electromagnetic wave on a scatterer in a hollow waveguide. We consider
radiation conditions and the solubility of the boundary-value problem for
Maxwell's equations in a cylinder. We study several spectral problems
connected with radiation conditions.
Citation:
A. L. Delitsyn, “The statement and solubility of boundary-value problems
for Maxwell's equations in a cylinder”, Izv. Math., 71:3 (2007), 495–544
\Bibitem{Del07}
\by A.~L.~Delitsyn
\paper The statement and solubility of boundary-value problems
for Maxwell's equations in a cylinder
\jour Izv. Math.
\yr 2007
\vol 71
\issue 3
\pages 495--544
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Linking options:
https://www.mathnet.ru/eng/im566
https://doi.org/10.1070/IM2007v071n03ABEH002366
https://www.mathnet.ru/eng/im/v71/i3/p61
This publication is cited in the following 15 articles:
B. A. Plamenevskii, A. S. Poretskii, O. V. Sarafanov, “Mathematical scattering theory in electromagnetic waveguides”, Izv. Math., 89:1 (2025), 50–105
B. A. Plamenevskii, A. S. Poretskii, “The Maxwell system in nonhomogeneous anisotropic waveguides with slowly stabilizing characteristics of filling medium”, St. Petersburg Math. J., 34:4 (2023), 635–693
B. A. Plamenevskii, A. S. Poretskii, O. V. Sarafanov, “A method for approximate computation of waveguide scattering matrices”, Russian Math. Surveys, 75:3 (2020), 509–568
Delitsyn A.L., “Mathematical Problems of Radiation and Propagation in Electromagnetic Waveguides”, J. Commun. Technol. Electron., 64:12 (2019), 1323–1338
Smirnov Yu.G., Smolkin E.Yu., “Investigation of the Spectrum of the Problem of Normal Waves in a Closed Regular Inhomogeneous Dielectric Waveguide of Arbitrary Cross Section”, Dokl. Math., 97:1 (2018), 86–89
N. Filonov, “Maxwell operator in a cylinder with coefficients that do not depend on the longitudinal variable”, St. Petersburg Math. J., 30:3 (2019), 545–572
Smirnov Yu.G., Smol'kin E.Yu., “Operator Function Method in the Problem of Normal Waves in An Inhomogeneous Waveguide”, Differ. Equ., 54:9 (2018), 1168–1179
B. A. Plamenevskiǐ, A. S. Poretskiǐ, “The Maxwell system in waveguides with several cylindrical outlets to infinity and non-homogeneous anisotropic filling”, St. Petersburg Math. J., 29:2 (2018), 289–314
A. L. Delitsyn, “On the character of increase in the field upon resonance excitation of a waveguide”, Comput. Math. Math. Phys., 56:12 (2016), 2056–2061
Plamenevskii B.A., Poretskii A.S., “Electromagnetic Waveguides With Several Cylindrical Ends and Non-Homogeneous Anisotropic Filling”, Proceedings of the International Conference on Days on Diffraction 2016 (Dd), eds. Motygin O., Kiselev A., Kapitanova P., Goray L., Kazakov A., Kirpichnikova A., IEEE, 2016, 332–335
Yu. G. Smirnov, “Eigenvalue transmission problems describing the propagation of TE and TM waves in two-layered inhomogeneous anisotropic cylindrical and planar waveguides”, Comput. Math. Math. Phys., 55:3 (2015), 461–469
I. E. Mogilevskii, “Primenenie metoda smeshannykh konechnykh elementov i otsenki skorosti skhodimosti dlya rascheta elektromagnitnogo polya volnovoda s vkhodyaschimi rebrami”, Zh. vychisl. matem. i matem. fiz., 52:11 (2012), 2071–2079
A. L. Delitsyn, “On the completeness of the system of eigenvectors of electromagnetic waveguides”, Comput. Math. Math. Phys., 51:10 (2011), 1771–1776
Delitsyn A.L., “Completeness of a system of eigenvectors of quadratic operator sheaf in waveguide theory”, Moscow University Physics Bulletin, 66:2 (2011), 126–128
Balantsev I.A., Delitsyn A.L., “Vector functional spaces related to the electromagnetic diffraction problem in a conical domain and their properties”, Moscow University Physics Bulletin, 64:3 (2009), 255–261
Citation in format AMSBIB
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