Sentinels with given sensitivity

Abstract

This work is devoted to the identification of parameters in a problem of pollution modeled by a semi-linear parabolic equation. We use the notion of sentinels introduced by J. L. Lions, (Lions, J. L. 1992 Sentinelles pour les systèmes distribués à données incomplètes . Masson, Paris.) re-visited in a more general framework. We prove the existence of such sentinels by solving a problem of null controllability with constraint on the control. The key of our results is an observability inequality of Carleman type adapted to the constraint.