Controllability properties for some semilinear parabolic PDE with a   quadratic gradient term
  We study several controllability properties for some semilinear parabolic PDE with a quadratic gradient term. For internal distributed controls, it is shown that the system is approximately and null controllable. The proof relies on the Cole-Hopf transformation. The same approach is used to deal with initial controls. 
Luis A. Fern\'andez
math.OC