Insensitizing controls for a phase field system

In this paper, a nonlinear parabolic system modeling phase field phenomena is considered. This system consists of two coupled parabolic equations, the first one describes the temperature of the material and the second one describes a phase field function. Under small perturbations of the initial data, we study the existence of controls insensitizing the phase field function and acting only on the temperature equation. This problem is equivalent to the null controllability of a parabolic system, which is studied by means of duality arguments, Carleman estimates, and fixed point theorems.