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Zapiski Nauchnykh Seminarov POMI, 1998, Volume 250, Pages 49–61 (Mi znsl641)  
This article is cited in 5 scientific papers (total in 5 papers)

Visualization of waves in the Maxwell dynamical system (the BC-method)

M. I. Belisheva, A. K. Glasmanb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Saint-Petersburg State University
Full-text PDF (219 kB) Citations (5)
Abstract: The paper develops an approach to the Inverse Problems using their relations to the Boundary Control Theory (the BC-method). One of main tools of the approach is the so-called Amplitude Formula (AF) based upon the Geometrical Optics and properties of controllability of dynamical systems. The AF makes the waves propagating into a domain be visible for an external observer performing measurements at a boundary. In the paper a natural analog of the AF is obtained for a system governed by the Maxwell equations. As an auxilliary result, an approximate controllability of electric component of the system is established under some assumptions of geometrical character.
Received: 20.11.1997
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 102, Issue 4, Pages 4166–4174
DOI: https://doi.org/10.1007/BF02673847
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: M. I. Belishev, A. K. Glasman, “Visualization of waves in the Maxwell dynamical system (the BC-method)”, Mathematical problems in the theory of wave propagation. Part 27, Zap. Nauchn. Sem. POMI, 250, POMI, St. Petersburg, 1998, 49–61; J. Math. Sci. (New York), 102:4 (2000), 4166–4174
Citation in format AMSBIB
\Bibitem{BelGla98}
\by M.~I.~Belishev, A.~K.~Glasman
\paper Visualization of waves in the Maxwell dynamical system (the BC-method)
\inbook Mathematical problems in the theory of wave propagation. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 1998
\vol 250
\pages 49--61
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl641}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1701858}
\zmath{https://zbmath.org/?q=an:0984.78009}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 102
\issue 4
\pages 4166--4174
\crossref{https://doi.org/10.1007/BF02673847}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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