POLLUTION DETECTION FOR THE SINGULAR LINEAR PARABOLIC EQUATION

In this work, we are concerned by the problem of identification of noisy terms which arise in singular problem as for remote sensing problems, and which are modeled by a linear singular parabolic equation. For the reason of missing some data that could be arisen when using the traditional sentinel method, the later will be changed by a new sentinel method for attaining the same purpose. Such new method is a particular least square-like method which permits one to distinguish between the missing terms and the pollution terms. In particular, a sentinel method will be given here in its more realistic setting for singular parabolic prob-lems, where in this case, the observation and the control have their support in different open sets. The problem of finding a new sentinel is equivalent to finding singular optimality system of the least square control for the parabolic equation that we solve.