Simultaneous null controllability with constraints. Application to simultaneous sentinels with given sensitivity

Abstract

The notion of sentinel was introduced by J. L. Lions Lions in order to identify parameters in problem of pollution ruled by a semilinear evolution equation. He proved that the existence of such sentinels is reduced to the solution of null controllability problem. We present here some case of simultaneous sentinels for a system of two semilinear parabolic equations. We show that such sentinels exist if only if, simultaneous null controllability with constraints on the control problems for a system governed by two heat equations holds. The key of our results is an observability inequality of Carleman type.