In this paper, a quasi-linear parabolic equation with a diffusion term
dependent on the gradient to the state with Dirichlet boundary conditions is
considered. The goal of this paper is to prove the existence of control that
insensitizes the system under study which is the case that Xu Liu left open in
2012. It is well known that the insensitizing control problem is equivalent to
a null controllability result for a cascade system, which is obtained by
duality arguments, Carleman estimates, and the Right Inverse mapping theorem.
Also, some possible extensions and open problems concerning other quasi-linear
systems are presented