Exact controllability to the trajectories for parabolic PDEs with nonlocal nonlinearities

This paper deals with the analysis of the internal control of a parabolic PDE with nonlinear diffusion, nonlocal in space. In our main result, we prove the local exact controllability to the trajectories with distributed controls, locally supported in space. The main ingredients of the proof are a compactness-uniqueness argument and Kakutani’s Fixed-Point Theorem in a suitable functional setting. Some possible extensions and open problems concerning other nonlocal systems are presented.Ministerio de Economía y Competitividad (MINECO). Españ

Nonnegative multiplicative controllability for semilinear multidimensional reaction-diffusion equations

We consider a multidimensional semilinear reaction-diffusion equation and we obtain at any arbitrary time an approximate controllability result between nonnegative states using as control term the reaction coefficient, that is, via multiplicative controls