Etude des systemes hyperboliques a donnees manquantes

Abstract

Identi cation problems are consisting to nd the causes of a phenomenon from an obser-vation, the resolution of this problem is doing by an experimental measurement. We suggest -in this these- to study a class of problems governed by hyperbolic equations with incomplete data. For this purpose we use the concept of sentinel introduced by J. L. Lions which is the best strategy to get answered about the causes from a weighted average of the observation. So we prove the existence of the sentinel function by solving a problem of null-controllability with constraints on the control. Then we are concerned with the identi cation of the terms of pollution present on the boundary of a system Petrowsky with a missing data.