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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 4, Pages 861–875 (Mi smj2244)  

This article is cited in 4 scientific papers (total in 4 papers)

A stability estimate for a solution to an inverse problem of electrodynamics

V. G. Romanov

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (302 kB) Citations (4)
References:
Abstract: We consider the integrodifferential system of equations of electrodynamics which corresponds to a dispersive nonmagnetic medium. For this system we study the problem of determining the spatial part of the kernel of the integral term. This corresponds to finding the part of dielectric permittivity depending nonlinearly on the frequency of the electromagnetic wave. We assume that the support of dielectric permittivity lies in some compact domain $\Omega\subset\mathbb R^3$. In order to find it inside $\Omega$ we start with known data about the solution to the corresponding direct problem for the equations of electrodynamics on the whole boundary of $\Omega$ for some finite time interval. On assuming that the time interval is sufficiently large we estimate the conditional stability of the solution to this inverse problem.
Keywords: equations of electrodynamics, inverse problem, stability, uniqueness.
Received: 29.03.2011
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 4, Pages 682–695
DOI: https://doi.org/10.1134/S0037446611040124
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: V. G. Romanov, “A stability estimate for a solution to an inverse problem of electrodynamics”, Sibirsk. Mat. Zh., 52:4 (2011), 861–875; Siberian Math. J., 52:4 (2011), 682–695
Citation in format AMSBIB
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\by V.~G.~Romanov
\paper A stability estimate for a~solution to an inverse problem of electrodynamics
\jour Sibirsk. Mat. Zh.
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\vol 52
\issue 4
\pages 861--875
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\transl
\jour Siberian Math. J.
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\vol 52
\issue 4
\pages 682--695
\crossref{https://doi.org/10.1134/S0037446611040124}
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  • https://www.mathnet.ru/eng/smj/v52/i4/p861
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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    Abstract page:410
    Full-text PDF :105
    References:73
    First page:3
     
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