Exact boundary controllability of Maxwell's equations with weak conductivity in the heterogeneous medium inside a general domain

This paper considers the question of control of Maxwell’s Equations (ME) in a non-homogeneous medium with positive conductivity by means of boundary surface currents applied over the entire boundary. The domain is assumed to be a bounded simply connected "star-shaped" region in R3 with smooth boundary. Using the Hilbert Uniqueness Method (HUM) of Lions, the exact boundary controllability over a sufficiently long time period is established in this case, provided that both the size of conductivity term and the spatial gradient of conductivity to electric permittivity ratio are small enough to satisfy a certain technical inequality. The restriction on conductivity size remains even when the medium is homogeneous.