Constrained Observability for Parabolic Systems

Abstract The objective of this paper is to develop the question of the constrained observability for distributed parabolic system evolving in spatial domain Ω. It consists in the reconstruction of the initial state and must be between two prescribed functions in a subregion ω of Ω. We give definitions and some properties of this kind of regional observability and we describe two reconstruction approaches where the first is based on subdifferential techniques and the second uses the lagrangian multiplier method. This last approach leads to an algorithm which is performed by example and simulation. Mathematics Subject Classification: 93B07, 93C2