INVERSE PROBLEMS FOR GENERAL PARABOLIC SYSTEMS AND APPLICATION TO ORNSTEIN-UHLENBECK EQUATION

We investigate the link between inverse problems and final state observability for a general class of parabolic systems. We generalize a stability result for initial data known for the case of self-adjoint dissipative operators. More precisely, we consider a system governed by an analytic semigroup. Under the assumption of final state observability, we prove a logarithmic stability estimate depending on the analyticity angle of the semigroup. This is done by using a general logarithmic convexity result. The abstract result is illustrated by considering the Ornstein-Uhlenbeck equation.