Truncated nonconvex state-dependent sweeping process: implicit and semi-implicit adapted Moreau’s catching-up algorithms

Abstract

In this paper, we deal with the existence of solutions for perturbed state-dependent Moreau’s sweeping processes. Two ways are investigated to realize such a study, depending on the nature of the used scheme, namely implicit or semi-implicit. In both cases, our evolution problem is described in a general Hilbert space by a prox-regular moving set controlled through the truncated Hausdorff–Pompeiu distance. The normal cone involved is perturbed by a sum of a single-valued mapping and a multimapping.