Inverse Problem and Null-Controllability for Parabolic Systems

In this paper, we present some abstract results giving a general connection between null-controllability and several inverse problems for a class of parabolic equations. We obtain some conditional stability estimates for the inverse problems consisting of determining the initial condition and the source term, from interior or boundary measurements. We apply this framework for Stokes system with interior and boundary observations, for a coupling of two Stokes system and a linear fluid-structure system. © de Gruyter 2011.