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.
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Guo et al. (2005) studied this question.