Phaseless problem of determination of anisotropic conductivity in electrodynamic equations

V. G. Romanov

Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 79-83

Résumé

or a system of electrodynamic equations corresponding to time-periodic oscillations, two inverse problems of determining anisotropic conductivity from given phaseless information on solutions of some direct problems are considered. It is supposed that the conductivity is described by a diagonal matrix $\sigma(x)=\operatorname{diag}(\sigma_1(x),\sigma_2(x),\sigma_3(x))$ such that $\sigma(x)=0$ outside of a compact domain $\Omega$. Plane waves coming from infinity are considered impinging on the inhomogeneity. To determine the unknown functions, the moduli of some components of the electric intensity vector of the total or scattered high-frequency electromagnetic fields are given on the boundary of $\Omega$. It is proved that this information reduces the inverse problems to problems of X-ray tomography.

Détail

Keywords: Maxwell equations, plane waves, phaseless inverse problem, anisotropy, conductivity, X-ray tomography.