Phase field systems with maximal monotone nonlinearities related to sliding mode control problems

We investigate phase field systems and Cahn-Hilliard systems perturbed by maximal monotone nonlinearities and singular terms. First, we prove existence, uniqueness and longtime behavior of the solution; then, we consider the related sliding mode control (SMC) problem: the main idea behind this scheme is first to identify a manifold of lower dimension (called the sliding manifold) where the control goal is fullled and such that the original system restricted to this sliding manifold has a desired behavior, and then to act on the system through the control in order to constrain the evolution on it, that is, to design a SMC-law that forces the trajectories of the system to reach the sliding surface and maintains them on it.