Exact boundary controllability of a shallow intrinsic shell model

We consider a variant of a Koiter shell model based on the intrinsic geometry methods of Michael Delfour and Jean-Paul Zolésio. This model, derived in [J. Cagnol, I. Lasiecka, C. Lebiedzik, J.-P. Zolésio, Uniform stability in structural acoustic models with flexible curved walls, J. Differential Equations 186 (1) (2003) 88–121], relies heavily on the oriented distance function which describes the geometry. Here, we establish continuous observability estimates in the Dirichlet case with an explicit observability time, under an additional shallowness assumption and a checkable geometric condition. This yields (by duality) exact controllability for this class of intrinsically modelled shells.