Systems determined by nonlinear operator valued measures and controlled by vector measures: Existence of optimal controls and necessary conditions of optimality Original Research Article

This is a summary of some results from recent papers of the author. Here we consider strongly nonlinear parabolic systems determined by nonlinear, monotone, hemicontinuous operator valued measures. We prove existence of solutions and their regularity properties and then consider optimal control problems, proving existence of optimal controls from the space of vector measures. Also we consider necessary conditions of optimality with or without state constraints. The paper is concluded with an example.