Journal of Convex Analysis 31 (2024), No. 4, 1165--1188
Copyright Heldermann Verlag 2024
Regularization of Nonconvex Integro-Differential Inclusions
Amira Lahmer
Laboratoire LMEPA, Faculté des Sciences Exactes et Informatique, Université de Jijel, Jijel, Algeria
lahmer.amiraa@gmail.com
Ilyas Kecis
Laboratoire LMEPA, Faculté des Sciences Exactes et Informatique, Université de Jijel, Jijel, Algeria
kecis_ilyas@yahoo.fr
Tahar Haddad
Laboratoire LMEPA, Faculté des Sciences Exactes et Informatique, Université de Jijel, Jijel, Algeria
haddadtr2000@yahoo.fr
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.
Keywords: Subdifferential, regularization, primal lower regular function, Moreau envelope, proximal mapping, Volterra integro-differential equation.
MSC: 49A52, 49J53, 34A60, 34G25, 34G20.
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