Non-convex second-order Moreau’s sweeping processes in Hilbert spaces

In this paper, we study a differential inclusion known as second-order sweeping process for a class of prox-regular non-convex sets. Assuming that such sets depend continuously on time and state, we give a new proof of the existence of solutions via Schauder’s fixed point theorem and the well-posedness for the perturbed first-order sweeping process in Hilbert spaces.