Null controllability for the parabolic equation with a complex principal part

The paper is devoted to a Study of the null controllability for the semilinear parabolic equation with a complex principal part. For this purpose, we establish it key weighted identity for partial differential operators (alpha + i beta)partial derivative(1) + Sigma(n)(j,k=1) partial derivative(k) (a(jk)partial derivative(j)) (with real functions alpha and beta), by which we develop I universal approach, based on global Carleman estimate, to deduce not only the desired explicit observability estimate for the linearized complex Ginzburg-Landau equation, but also all the known controllability/observability results for the parabolic, hyperbolic, Schrodinger and plate equations that are derived via Carleman estimates. (C) 2009 Elsevier Inc. All rights reserved.