The regularity of the wave equation with partial Dirichlet control and colocated observation

In this paper we analyze a multidimensional controlled wave equation on a bounded domain, subject to partial Dirichlet control and colocated observation. By means of a partial Fourier transform, it is shown that the system is well- posed and regular in the sense of D. Salamon and G. Weiss. The corresponding feedthrough operator is found to be the identity operator on the input space.