Existence, stability and optimality for optimal control problems governed by maximal monotone operators

We study optimal control problems governed by maximal monotone differential inclusions with mixed control-state constraints in infinite dimensional spaces. We obtain some existence results for this kind of dynamics and construct the discrete approximations that allows us to strongly approximate optimal solutions of the continuous-type optimal control problems by their discrete counterparts. Our approach allows us to apply our results for a wide class of mappings that are applicable in mechanics and material sciences.