Well-Posedness of Some Evolution Problems in the Theory of Automatic Feed-Back Control for Systems with Distributed Parameters

The subject of this paper is the evolution, in time, of systems of diffusion type controlled by an automatic feed-back mechanism using a finite number of observators and control-inputs. For the initial-boundary value problem for a functional partial differential equation of parabolic type, which the state variable has to satisfy, the following types of questions are considered: existence, uniqueness, regularity and continuous dependence on data of a solution. Answers to these questions are given in function spaces of Holder and Sobolev type.