Dynamical inverse problem for the Maxwell system: Recovering the velocity in the regular zone (the BC-method) (Q2704037)

The paper is devoted to the 3D dynamical inverse problem for the Maxwell system in a bounded domain with smooth boundary. It is assumed that the dielectric and magnetic permeabilities \(\varepsilon\), \(\mu\) are smooth positive functions. The inverse problem consists in recovering the velocity function \(c:= (\varepsilon\mu)^{-1/2}\) from the response operator of the corresponding initial-boundary value problem. The main result is that \(c\) is uniquely determined in a boundary layer by means of this response operator and the values of \(c\) and its normal derivative on the boundary. The paper is a detailed version of the authors' preprint [Boundary control and inverse problem for the dynamical Maxwell system: the recovering in the regular zone, Preprint CMLA ENS Cachan no. 9814 (1998)].