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.
Asymptotic Stability of POD based Model Predictive Control for a semilinear parabolic PDE
A Hopf-Lax splitting approximation for semilinear parabolic PDEs with convex and quadratic growth gradients
Controllability properties of a class of systems modeling swimming microscopic organisms
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