Controllability under positivity constraints for non-linear and non-local parabolic PDEs

This article studies the control of a non-local and non-linear parabolic PDE. The tools to develop the control study are: regularity in Holder spaces, parabolic regularity, Carleman and Observability inequalities, compactness, stability and the Kakutani Fixed Point method. We obtain three results about controllability. first, local results in H\"older spaces; second, restriction on the control signal with target trajectories; and third, positivity of the minimal controllability time. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/96/abstr.html