Observability inequalities for shallow shells

We consider some observability inequalities from boundary for a general sha llow shell with a middle surface of any shape. At first, an estimate is est ablished by the geometric multiplier method in the case that no boundary co nditions are imposed under some checkable geometric conditions. Then our re sults yield continuous observability estimates for two kinds of boundary co nditions which have a physical meaning with an explicit observability time and hence, by duality, exact controllability results.