Regularization of Nonconvex Sweeping Process in Hilbert Space

Abstract

This paper deals with the differential inclusion of sweeping process associated, on an interval I, with the normal cone to a moving set C(t). Under a Lipschitzian variation of the set-valued mapping C(·) and under the prox-regularity assumption of C(t), it is shown that one can regularize the sweeping process to obtain a family of classical differential equations whose solutions exist on a fixed appropriate interval and converge to the solution of the sweeping process on this interval. The general case where C(t) moves in an absolutely continuous way is reduced to the previous one to obtain the existence and uniqueness of solution on all the interval I.