An existence result for integro-differential degenerate sweeping process with convex sets

Year 2025, Volume: 54 Issue: 3, 845 - 868, 24.06.2025

Mohamed Kecies

https://doi.org/10.15672/hujms.1449554

Abstract

In this paper, we study the well-posedness in the sense of existence and uniqueness of a solution of integrally perturbed degenerate sweeping processes, involving convex sets in Hilbert spaces. The degenerate sweeping process is perturbed by a sum of a single-valued map satisfying a Lipschitz condition and an integral forcing term. The integral perturbation depends on two time-variables, by using a semi-discretization method. Unlike the previous works, the Cauchy's criterion of the approximate solutions is obtained without any new Gronwall's like inequality.

Keywords

degenerate sweeping process , perturbation , differential inclusion , set-valued map , normal cone , maximal monotone operator , Volterra integro-differential equation

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