Controllability of linear and semilinear non-diagonalizable parabolic systems

Abstract

This paper is concerned with the controllability of some (linear and semilinear) non- diagonalizable parabolic systems of PDEs. We will show that the well known null controllability prop- erties of the classical heat equation are also satisfied by these systems at least when there are as many scalar controls as equations and some (maybe technical) conditions are satisfied. We will also show that, in some particular situations, the number of controls can be reduced. The minimal amount is then determined by a Kalman rank condition.