epsilon-insensitizing controls for pointwise observations of the heat equation

Abstract

In this paper, we study the epsilon-insensitizing controllability for the functional given by integrating in time the square of the solution of the heat equation in a finite number of points of the domain Omega subset of R-N, i.e., when the observation set is reduced to a finite set of points. We reduce the controllability problem to a unique continuation property for a cascade system of linear heat equations and we obtain a positive result in the case N less than or equal to 3. (C) 2003 Elsevier B.V. All rights reserved.