Regional Observability for Semilinear Distributed Parabolic Systems

The purpose of this paper is to explore the concept of regional observability for a class of semilinear distributed parabolic systems. Then we give an approach for the reconstruction of the state on a subregion of the evolution domain. We also study the variation of the estimated state error with respect to measurements errors. At last we present an approach based on fixed point techniques leading to a numerical approach which is successfully tested through an example.