New modification Sentinel for Linear Parabolic Equation

Abstract

The purpose of this article is, firstly, to modify the old definition of the sentinel, introduced by J.L. Lions, so that we can separate the control support to the observation support and, secondly, to identify the pollution terms which arise in regular problems which are modeled by a linear parabolic equation. A new modification of the sentinel is used to identify pollution terms in the general case where the observation and the control supports are disjoint. The problem of finding a new modification sentinel is equivalent to finding the unique control of regular adjoint system of the parabolic equation that we solve.