naa a22 4500 510811787 CHVBK 20180411083445.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813020120 doi (NATIONALLICENCE)springer-10.1134/S0081543813020120 Romanov V. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, 630090, Novosibirsk, Russia aut A two-dimensional inverse problem for an integro-differential equation of electrodynamics [Elektronische Daten] [V. Romanov] An integro-differential equation corresponding to a 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 integro-differential 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 Ω ⊂ ℝ2. To find this coefficient inside Ω, we use information on the solution of the corresponding direct problem on the boundary of Ω 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. Pleiades Publishing, Ltd., 2013 inverse problem nationallicence electrodynamics equations nationallicence hyperbolic equation nationallicence stability nationallicence uniqueness nationallicence Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 151-157 0081-5438 280<151 2013 280 11501 https://doi.org/10.1134/S0081543813020120 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813020120 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Romanov V. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, 630090, Novosibirsk, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280(2013-04-01), 151-157 0081-5438 280<151 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer