A coupled problem described by time-dependent subdifferential operator and non-convex perturbed sweeping process

Abstract

The aim of the present paper is to state the well-posedness of a new dynamical system driven by a differential inclusion involving time-dependent subdifferential operators with integral perturbation and a non-convex perturbed sweeping process. The current study is motivated by recent works on integro-differential sweeping processes and dynamical systems coupled by differential inclusions (involving sweeping processes and maximal monotone operators). In our development, we proceed using a discretization method, combining tools of first-order evolution problems of subdifferential type and those governed by the normal cone of $ r $-prox regular moving sets. We establish a new existence result to the class of dynamical systems under consideration, in the context of infinite dimensional Hilbert setting. This allows us to deal with a Bolza-type problem in optimal control theory.