The dynamical 3-dimensional inverse problem for the Maxwell system

Abstract:

The problem of recovering the scalar electric permittivity and magnetic permeability (respectively, $\varepsilon$ and $\mu$) of a medium in a bounded domain $\Omega \subset {\mathbb R}^3$ by the boundary measurements on $\partial \Omega$ is considered. As data, the value of the velocity $c=(\varepsilon \mu )^{-1/2}$ with its normal derivative on $\partial \Omega$ is taken, along with the response operator, which maps the tangential part $e_\theta \mid _{\partial \Omega \times [0,2T]}$ of the electric field on the boundary to the tangential part $h_\theta \mid _{\partial \Omega \times [0,2T]}$ of the magnetic field ($2T$ is the duration of measurements). With the help of the BC-method, it is established that the described data uniquely determine $\varepsilon$ and $\mu$ in the near-boundary layer with optical thickness $T$, provided that the domain satisfies some geometric condition.