Controllability Of Semilinear Parabolic Equations Under Bounded Constraint

Up to now,there are many papers deal with the controllability of the semilinear parabolic system without any constraint on the controller.This paper is concerned with the null controllability of a semilinear parabolic system under bounded L~2-constraint.The methods we use combine observability inequalities,energy estimates for parabolic equations and the dual theory.