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

  • Moumini Kere
  • Ousseynou Nakoulima Universit√© des Antilles et de la Guyane


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.