Year: 2025
Type: article
Abstract: In this paper, we study a discontinuous sweeping process involving prox-regular sets and a multivalued perturbation in a separable Hilbert space. The variation of the moving set is controlled by a positive Radon measure and the values of the perturbation are closed, not necessarily convex sets. A solution of the sweeping process is a pair consisting of a right continuous function of bounded variation whose differential measure is absolutely continuous with respect to some positive Radon measure and an integrable selector of theperturbation considered on this function.Along with the original perturbation we consider the perturbation with the convexified values. We prove theorems of existence and relaxation of solutions. The latter means the density of the solution set of the sweeping process with the original perturbation in the solution set of the sweeping process with the convexified perturbation.
DOI: 10.3934/eect.2025031
Authors: Alexandr Alexandrovich Tolstonogov, Igor Vyacheslavovich Bychkov
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409208034