Simultaneous null controllability with two constraints. Application to simultaneous discriminating sentinel with given sensitivity

Abstract

We present here some case of simultaneous sentinels for a system of two semilinear parabolic equations. We show that such sentinels exist if, and only if, simultaneous null controllability with two constraints on the control problem for a system governed by two heat equations holds. The key of our results is an observability inequality of Carleman type.