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

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 systèmes distribués a données incomplètes, 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.