EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR AN INTEGRAL PERTURBATION OF MOREAU’S SWEEPING PROCESS

We prove existence and uniqueness of solutions for a sweeping process driven by a prox-regular moving set with an integral forcing term, where the integrand is Lipschitz with respect to the state variable. The problem is motivated by a model introduced by Brenier, Gangbo, Savare' and Westdickenberg [Sticky particle dynamics with interactions, J. Math. Pures Appl. 99 (2013)]. The proof is based on a general type of penalization