  The aim of this paper is to extend the concept of regional exponential
general observability to the case of Neumann boundary conditions problem in
diffusion system. More precisely, for linear distributed parameter diffusion
systems, we show that the sensors characterizations allow to reconstruct the
regional exponential state in a sub-region of the considered systems domain.
Moreover, various interesting results associated with the choice of sensors are
given and illustrated in specific situations in order regional exponential
general observability notion to be achieved. Finally, we also show that, there
exists a dynamical system for diffusion system is not exponential general
observable in the usual sense, but it may be regional exponential general
observable.
