Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Subdifferential
  • regularization
  • primal lower regular function
  • Moreau envelope
  • proximal mapping
  • Volterra integro-differential equation

Mathematics Subject Classification

49A52, 49J53, 34A60, 34G25, 34G20

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Suggested citation

A. Lahmer, I. Kecis, T. Haddad. “Regularization of Nonconvex Integro-Differential Inclusions.” Journal of Convex Analysis 31 (2024), No. 4, 1165–1188. https://doi.org/10.68381/jca31057

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press.