On the controllability of some systems of wave equations.

The controllability of a system consists in using a source term to drive the system from a given initial state to a final desired state. The controllability of a single wave equation is well understood now. However, when it comes to systems of two or more wave equations, their controllability is still at an early stage; much work is needed. First, I shall review what is known at this point. Then I will concentrate  on the controllability of two coupled wave equations with potential terms when the control acts on a suitable portion of the domain under consideration. The controllability problem will be reduced to an inverse inequality for the adjoint system. The use of the Carleman estimate to prove such an inequality will be addressed. Some open problems will wrap up the talk.