Application de la sentinelle au systeme dynamique de la desertification.

Abstract

This work is devoted to find, among all the bounded operators B, the one which gives a maximal controllability, in the sense that the operator image Hu=∫S(T-s)Bu(s)ds is maximal in the state space, following the inclusion order relation, where S is a semi-group defined on the state space of a parabolic system. The proposed method is based on the construction of the order relation, in the space of classes of bounded operators, from the inclusion order relation and also on the application of Zorn's lemma. On the other hand, new actuators that allow us to simplify the conditions of the weak controllability of Al Jai have been choosen. The developping idea consists in a reduction of conditions introduced by Al Jai in such a way that weak controlability properties are reserved.