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This article is cited in 4 scientific papers (total in 4 papers)
MATHEMATICS
Problem of determining the anisotropic conductivity in electrodynamic equations
V. G. Romanovab a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
b Mathematical Center in Akademgorodok, Novosibirsk, Russian Federation
Abstract:
For a system of electrodynamic equations, the inverse problem of determining an anisotropic conductivity is considered. It is supposed that the conductivity is described by a diagonal matrix $\sigma(x)=\operatorname{diag}(\sigma_1(x),\sigma_2(x),\sigma_3(x))$ with $\sigma(x)$ outside of the domain $\Omega=\{x\in\mathbb R^3\mid |x|<R\}$, $R>0$, and the permittivity $\varepsilon$ and the permeability $\mu$ of the medium are positive constants everywhere in $\mathbb R^3$. Plane waves coming from infinity and impinging on an inhomogeneity localized in $\Omega$ are considered. For the determination of the unknown functions $\sigma_1(x),\sigma_2(x),\sigma_3(x)$, information related to the vector of electric intensity is given on the boundary $S$ of the domain $\Omega$. It is shown that this information reduces the inverse problem to three identical problems of X-ray tomography.
Keywords:
Maxwell equations, anisotropy, conductivity, plane waves, inverse problem, tomography.
Received: 03.11.2020 Revised: 02.12.2020 Accepted: 07.12.2020
Citation:
V. G. Romanov, “Problem of determining the anisotropic conductivity in electrodynamic equations”, Dokl. RAN. Math. Inf. Proc. Upr., 496 (2021), 53–55; Dokl. Math., 103:1 (2021), 44–46
Linking options:
https://www.mathnet.ru/eng/danma153 https://www.mathnet.ru/eng/danma/v496/p53
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