Nonconvex integro-differential sweeping processes involving maximal monotone operators

Year 2023, Volume: 52 Issue: 6 - Special Issue: Nonlinear Evolution Problems with Applications, 1677 - 1690, 03.11.2023

Mouchira Mansour , Ilyas Kecis Tahar Haddad

https://doi.org/10.15672/hujms.1197368

Abstract

This paper is devoted to the study of a perturbed differential inclusion governed by a nonconvex sweeping process in a Hilbert space. The sweeping process is perturbed by a sum of an integral forcing term which the integrand depends on two time-variables and a maximal monotone operator. By using a semi-regularization method combined with a Gronwall-like inequality we prove solvability of the initial value problem.

Keywords

Moreau’s sweeping process, Volterra integro-differential equation, Maximal monotone operator, differential inclusion, variational analysis

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