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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2012, Volume 18, Number 1, Pages 273–280 (Mi timm796)  

This article is cited in 3 scientific papers (total in 3 papers)

Two-dimensional problem for an integrodifferential equation of electrodynamics

V. G. Romanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (156 kB) Citations (3)
References:
Abstract: An integrodifferential equation corresponding to the two-dimensional problem of electrodynamics with dispersion is considered. It is assumed that the electrodynamic properties of a nonconducting medium with a constant magnetic permeability and the external current are independent of the $x_3$ coordinate. In this case, the third component of the electric field vector satisfies a second-order scalar integrodifferential equation with a variable permittivity of the medium. For this equation, we study the problem of finding the spatial part of the kernel entering the integral term. This corresponds to finding the part of the permittivity that depends on the electromagnetic frequency. It is assumed that the permittivity support is contained in some compact domain $\Omega\subset\mathbb R^2$. To find this coefficient inside $\Omega$, we use information on the solution of the corresponding direct problem on the boundary of $\Omega$ on a finite time interval. An estimate for the conditional stability of the solution of the inverse problem is established under the assumption that the time interval is sufficiently large.
Keywords: inverse problem, electrodynamics equations, hyperbolic equation, stability, uniqueness.
Received: 25.01.2011
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2013, Volume 280, Issue 1, Pages 151–157
DOI: https://doi.org/10.1134/S0081543813020120
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: V. G. Romanov, “Two-dimensional problem for an integrodifferential equation of electrodynamics”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 1, 2012, 273–280; Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 151–157
Citation in format AMSBIB
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\by V.~G.~Romanov
\paper Two-dimensional problem for an integrodifferential equation of electrodynamics
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 1
\pages 273--280
\mathnet{http://mi.mathnet.ru/timm796}
\elib{https://elibrary.ru/item.asp?id=17358695}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2013
\vol 280
\issue , suppl. 1
\pages 151--157
\crossref{https://doi.org/10.1134/S0081543813020120}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84875995759}
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  • https://www.mathnet.ru/eng/timm/v18/i1/p273
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    References:63
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