Well-posedness and regularity of Naghdi's shell equation under boundary control and observation

A system of Naghdi's shell equation with Dirichlet boundary control and collocated observation is considered. Results on the associated nonhomogeneous boundary value problem are presented. Based on these results, it is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The expression of the corresponding feedthrough operator is explicitly found by means of Riemannian geometric method and partial Fourier transform. These properties make this partial differential control system parallel in many ways finite-dimensional ones in the general framework of well-posed and regular infinite-dimensional systems.