Regularization of Nonconvex Integro-Differential Inclusions

This paper is concerned with the regularization of the dynamical differential inclusion governed by the subdifferential of a function Φ perturbed both by a Carathéodory mapping and by an integral forcing term. The integrand of the forcing term depends on two time-variables. It is shown that when the function Φ is primal lower regular, one can regularize the differential inclusion by a family of new integro-differential equations which are well posed. The family of solutions of the regularized integro-differential equations is shown to converge uniformly to a (local and global) solution of the differential inclusion.