Problem of determining the anisotropic conductivity in electrodynamic equations

V. G. Romanov

Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 53-55

Résumé

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.

Détail

Keywords: Maxwell equations, anisotropy, conductivity, plane waves, inverse problem, tomography.