Null Controllability of Some Systems of Two Parabolic Equations with One Control Force

Abstract

In this paper we establish some exact controllability results for systems of two parabolic equations. First, we prove the existence of insensitizing controls for the $L^2$ norm of the gradient of solutions of linear heat equations. Then, in the worst situation where null controllability for a system of two parabolic equations can hold, we prove this result for some general couplings.