Geodesic
Problem of determining the anisotropic conductivity in electrodynamic equations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 53-55

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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 $\Omega=\{x\in\mathbb R^3\mid |x|$, $R>0$, 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. 
V. G. Romanov. Problem of determining the anisotropic conductivity in electrodynamic equations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 53-55. http://geodesic.mathdoc.fr/item/DANMA_2021_496_a10/
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