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In this paper, a quasi-linear parabolic equation with a diffusion termdependent on the gradient to the state with Dirichlet boundary conditions isconsidered. The goal of this paper is to prove the existence of control thatinsensitizes the system under study which is the case that Xu Liu left open in2012. It is well known that the insensitizing control problem is equivalent toa null controllability result for a cascade system, which is obtained byduality arguments, Carleman estimates, and the Right Inverse mapping theorem.Also, some possible extensions and open problems concerning other quasi-linearsystems are presented.

Insensitizing controls for a quasi-linear parabolic equation with diffusion depending on gradient of the state