Regularization of controllability problems and observability problems for distributed parameter systems of parabolic type

The purpose of this paper is to investigate the controllability problem and the observability problem for a distributed parameter system of parabolic type. For a distributed parameter system of parabolic type, both problems are not well-posed in general. A well-posed approximation method which regularizes the problems is presented. The method is analyzed under the assumption that the system is controllable at time T and observable at time T.