On the uniqueness of the recovery of parameters of the Maxwell system from dynamical boundary data
The paper deals with the inverse problem to recover the smooth dielectric and magnetic permeabilities \(\epsilon\) and \(\mu\) of the time-dependent Maxwell system from dynamical boundary data. Maxwell's equation are considered in a bounded domain with smooth boundary, zero initial values and with Dirichlet condition for the tangent component of the electric field. The authors prove that the permeabilities can be determined uniquely in the entire domain from the response operator which maps the tangent component of the electric field on the boundary to the tangent component of the magnetic field. It is sufficient that the response is given for a sufficiently large, but finite time interval. The theorem is based on the Holmgren-John-Tataru theorem for the Maxwell system.
scientific article; zbMATH DE number 2183294