Exact controllability of wave equations in Rn coupled in parallel

We consider a system of two parallel identical wave equations in Rn coupled by a distributed internal dissipator. It is shown that despite the distributed damping, there exists a subspace of states which is unstable. We prove an exact controllability result with Dirichlet boundary controls with no restrictions on the coupling parameters, with a control time that is independent of the coupling constants and dictated by geometric optics.