Contribution to the study of certain evolution problems

Abstract

In this thesis, we are interested in the well-posedness of a new class of differential inclusion driven by time-dependent subdifferential operators with integral perturbation in Hilbert space. In the first part, we handle some coupled systems by such a class and fractional differential equations. This result is obtained using Schauder’s fixed point theorem. In the second part, we establish the existence and uniqueness of the solution to a system governed by a differential inclusion involving the subdifferential operator with an integral perturbation and a non-convex perturbed sweeping process. Our approach is based on a discretization method. As an application of this result, a Bolza-type problem in optimal control theory is therefore studied.