(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2015)
The regional exponential reduced observability concept in the presence for linear dynamical systems is addressed for a class of distributed parameter systems governed by strongly continuous semi group in Hilbert space. Thus, the existence of necessary and sufficient conditions is established for regional exponential reduced estimator in parabolic infinite dimensional systems. More precisely, the introduced approach is developed by using the decomposed system and reduced system in connection with various new concepts of (stability, detectability, estimator, observability and strategic sensors). Finally, we also show that there exists a dynamical system for two-phase exchange system described by the coupled parabolic equations is not exponentially reduced observable in usual sense, but it may be regionally exponentially reduced observable.