A prox-regular sweeping process coupled with a maximal monotone differential inclusion

A coupled system consisting of a sweeping process and an evolution maximal monotone inclusion is considered. The values of moving set of the sweeping process are prox-regular sets that depend on time and state of the system. The right-hand side of the sweeping process contains the sum of two multivalued time- and state-dependent perturbations with different semicontinuity properties. The perturbation in the right-hand side of maximal monotone inclusion is a single-valued function. A solution to the sweeping process is a right continuous function of bounded variation (a BV-solution). A solution to the maximal monotone inclusion is an absolutely continuous function. A theorem on existence of a solution to this system is proved, and when the perturbations are convex, a theorem on compactness of the solution set is established.