PARTIAL NULL CONTROLLABILITY OF PARABOLIC LINEAR SYSTEMS

This paper is devoted to the partial null controllability issue of parabolic linear systems with n equations. Given a bounded domain Omega in R-N (N is an element of N*), we study the effect of m localized controls in a nonempty open subset omega only controlling p components of the solution (p,m n). The first main result of this paper is a necessary and sufficient condition when the coupling and control matrices are constant. The second result provides, in a first step, a sufficient condition of partial null controllability when the matrices only depend on time. In a second step, through an example of partially controlled 2 x 2 parabolic system, we will provide positive and negative results on partial null controllability when the coefficients are space dependent.