Approximate controllability-application to approached sentinel

Abstract

We consider here a semilinear heat equation with the source term as well as the initial and boundary conditions are partially known. We are interesting in a sentinel [6] problem, which consists in finding the pollution term withou tany attempt of computing the perturbation. We present her some case of approched sentinels. We prove the existence of such sentinel by solving a problem of approximate controllability. To deal with the approximate controllability problem, we make use of the theory of duality in convex optimization following Fenchel-Rockafellar.