A null controllability problem with constraint on the control deriving from boundary discriminating sentinels

This paper is devoted to the detection of boundary pollution in a pollution problem modeled by a semilinear parabolic equation. We use the notion of discriminating sentinels introduced by Lions in [J.L. Lions, Sentinelles pour les systemes distribues a donnees incompletes, Masson, Paris, 1992], revisited in a more general framework. We show that establishing the existence of such sentinels is reduced to the solution of a null boundary controllability problem with constraint on the control. Our results are supported by an observability inequality of Carleman type adapted to the constraint. (C) 2009 Elsevier Ltd. All rights reserved.