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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 3, Pages 61–112 (Mi izv566)  

This article is cited in 11 scientific papers (total in 11 papers)

The statement and solubility of boundary-value problems for Maxwell's equations in a cylinder

A. L. Delitsyn

M. V. Lomonosov Moscow State University, Faculty of Physics

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.


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English version:
Izvestiya: Mathematics, 2007, 71:3, 495–544

Bibliographic databases:

UDC: 517.95
MSC: 78A40, 35Q60
Received: 01.12.2004
Revised: 22.09.2006

Citation: A. L. Delitsyn, “The statement and solubility of boundary-value problems for Maxwell's equations in a cylinder”, Izv. RAN. Ser. Mat., 71:3 (2007), 61–112; Izv. Math., 71:3 (2007), 495–544

Citation in format AMSBIB
\by A.~L.~Delitsyn
\paper The statement and solubility of boundary-value problems
for Maxwell's equations in a cylinder
\jour Izv. RAN. Ser. Mat.
\yr 2007
\vol 71
\issue 3
\pages 61--112
\jour Izv. Math.
\yr 2007
\vol 71
\issue 3
\pages 495--544

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    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    2. A. L. Delitsyn, “On the completeness of the system of eigenvectors of electromagnetic waveguides”, Comput. Math. Math. Phys., 51:10 (2011), 1771–1776  mathnet  crossref  mathscinet  isi
    3. 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  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    4. 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  mathnet
    5. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. 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  mathnet  crossref  crossref  isi  elib
    7. 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  crossref  isi  scopus
    8. 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  mathnet  crossref  mathscinet  isi  elib
    9. 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  crossref  zmath  isi  scopus
    10. N. Filonov, “Operator Maksvella v tsilindre s koeffitsientami, ne zavisyaschimi ot prodolnoi peremennoi”, Algebra i analiz, 30:3 (2018), 210–249  mathnet  elib
    11. 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  crossref  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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