Controllability for transmission wave/plate equations on Riemannian manifolds

In this paper we consider controllability for transmission system of coupling wave equations with Euler–Bernoulli equations on Riemannian manifolds. We show that such a system is exactly controllable by boundary controls only along the exterior boundary, which means there is no control on the interface of the transmission system. Our proofs rely on the Hilbert Uniqueness Method (HUM) and geometric multiplier method.