ABSTRACT
In this chapter, we consider the active control of a pair of wave equations, each defined on different geometries: one wave equation holds on the interior of a bounded domain Ω; the other wave equation is satisified on a portion of the boundary Γ0 of ∂Ω. The respective wave equations are coupled by trace terms on the boundary interface Γ0. For this coupled system of equations, we present results of exact controllability in the case that the controllers are exerted strictly on the boundary ∂Ω. In particular, we give precise geometric conditions under which control on the “active portion” Γ0 only gives exact controllability for the dynamics of both wave equations, the interior as well as the boundary wave.
