Null controllability and numerical simulations for a class of degenerate parabolic equations with nonlocal nonlinearities

In this work, we prove a Carleman estimate, which allows us to obtain the local null-controllability for a class of strongly degenerate parabolic equations with nonlocal terms, naturally extending the main result of Demarque R et al. (Nonlin Anal: Real World Appl 43:523-547, 2018). We present a theoretical approach, applying Lyusternik's Inverse Function Theorem, as well as, some numerical experiments. We use Freefem++ (version 4.9) for the data computations. Motivated by Le Balc'H K (J de Mathematiques Pures et Appliquees 135:103-139, 2020), we prove a Poincare inequality type, applying it to conclude that our local null-controllability theorem implies a large global null-controllability one.