Insensitizing controls for some parabolic systems

This paper is addressed to establishing the existence of insensitizing controls for some parabolic systems. First, a class of nonlinear complex Ginzburg-Landau equations are investigated. When the nonlinearity satisfies a suitable superlinear growth condition at infinity, we prove the existence of insensitizing controls for the semilinear Ginzburg-Landau equation. Meanwhile, the insensitivity problem of one-dimensional fourth order linear parabolic equations is studied. The key is to establish the controllability for a coupled fourth order parabolic system by only one control.