Radiation and scattering in electromagnetic waveguides near thresholds
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B. A. Plamenevskii and A. S. Poretskii
Translated by: the authors - St. Petersburg Math. J. 32 (2021), 781-807
- DOI: https://doi.org/10.1090/spmj/1670
- Published electronically: July 9, 2021
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Abstract:
A waveguide occupies a three-dimensional domain $G$ with several cylindrical outlets to infinity and is described by the stationary Maxwell system with perfectly conductive boundary conditions. It is assumed that the medium filling the waveguide is homogeneous and isotropic at infinity in a limiting sense. The paper is devoted to description of the behavior of the scattering matrix, radiation conditions, and solutions as the spectral parameter tends to a threshold. In particular, it is shown that the scattering matrix has finite one-sided limits at every threshold and the limits are expressed in terms of the “scattering matrix stable near the threshold”.References
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Bibliographic Information
- B. A. Plamenevskii
- Affiliation: St. Petersburg State University, Universitetskaya Emb. 7/9, 199034 St. Petersburg, Russia
- Email: b.plamenevskii@spbu.ru
- A. S. Poretskii
- Affiliation: St. Petersburg State University, Universitetskaya Emb. 7/9, 199034 St. Petersburg, Russia
- Email: a.poretsky@spbu.ru
- Received by editor(s): September 13, 2019
- Published electronically: July 9, 2021
- Additional Notes: Supported by Russian Science Foundation, grant no. 17-11-01126
- © Copyright 2021 American Mathematical Society
- Journal: St. Petersburg Math. J. 32 (2021), 781-807
- MSC (2020): Primary 35Q61
- DOI: https://doi.org/10.1090/spmj/1670
- MathSciNet review: 4167869
Dedicated: Dedicated to Nina Nikolaevna Ural’tseva on the occasion of her anniversary