We present a generalization of the Kalman rank condition to the case of n×n linear parabolic systems with constant coefficients and diagonalizable diffusion matrix. To reach the result, we are led to prove a global Carleman estimate for the solutions of a scalar 2n−order parabolic equation and deduce from it an observability inequality for our adjoint system. AMS 2000 subject classification: 93B05, 93B07, 35K05, 35K55, 35R30.

This work is concerned with the null-controllability of semilinear parabolic systems by a single control force acting on a subdomain.

Abstract.We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.Mathematics Subject Classification. 93B05, 93C20, 93C25, 35K90.