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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

The Maxwell system in waveguides with several cylindrical outlets to infinity and nonhomogeneous anisotropic filling


Authors: B. A. Plamenevskiĭ and A. S. Poretskiĭ
Translated by: B. A. Plamenevskiĭ
Original publication: Algebra i Analiz, tom 29 (2017), nomer 2.
Journal: St. Petersburg Math. J. 29 (2018), 289-314
MSC (2010): Primary 35Q61
DOI: https://doi.org/10.1090/spmj/1494
Published electronically: March 12, 2018
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Abstract: A waveguide occupies a domain $ G$ in $ \mathbb{R}^3$ with several cylindrical outlets to infinity; the boundary $ \partial G$ is assumed to be smooth. The dielectric $ \varepsilon $ and magnetic $ \mu $ permittivities are matrix-valued functions smooth and positive definite in $ \overline {G}$. At every cylindrical outlet, the matrices $ \varepsilon $ and $ \mu $ tend, at infinity, to limit matrices independent of the axial variable. The limit matrices can be arbitrary smooth and positive definite matrix-valued functions of the transverse coordinates in the corresponding cylinder. In such a waveguide, the stationary Maxwell system with perfectly conducting boundary conditions and a real spectral parameter is considered. In the presence of charges and currents, the corresponding boundary value problem with radiation conditions turns out to be well posed. A unitary scattering matrix is also defined. The Maxwell system is extended to an elliptic system. The results for the Maxwell system are derived from those obtained for the elliptic problem.


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Additional Information

B. A. Plamenevskiĭ
Affiliation: St. Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia
Email: b.plamenevskii@spbu.ru

A. S. Poretskiĭ
Affiliation: St. Petersburg State University, Universitetskaya nab. 7/9, 199034 St. Petersburg, Russia
Email: st036768@student.spbu.ru

DOI: https://doi.org/10.1090/spmj/1494
Keywords: Radiation principle, scattering matrix, elliptic extension
Received by editor(s): October 10, 2016
Published electronically: March 12, 2018
Dedicated: To the memory of V. S. Buslaev
Article copyright: © Copyright 2018 American Mathematical Society

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