State dependent nonconvex sweeping processes in smooth Banach spaces
type: Item
instance of: scholarly article
title: State dependent nonconvex sweeping processes in smooth Banach spaces
zbMATH Open document ID: 1479.34115
DOI: 10.4171/PM/2049
author: Djalel Bounekhel
author: Messaoud Bounkhel
author: Mostafa Bachar
published in: Portugaliae Mathematica. Nova Série
publication date: 2021-05-14T00:00:00Z
review text: In this paper, the authors prove the existence of the solution for a state dependent nonconvex sweeping process (SDNSP), represented by the following multivalued differential equation \[ -\frac{d}{dt} J(u(t))\in N^{C}(t,u(t);u(t))\;\text{ for a.e. } t\in [0,T], \] where \(N^{C}\) stands for the Clarke normal cone. The context is that of a \(2\)-uniformly smooth and \(q\)-uniformly convex Banach space. A perturbed state dependent nonconvex sweeping process is also considered. The results extend recent existing results from the setting of Hilbert spaces to the setting of Banach spaces.
reviewed by: Adrian Petruşel
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49J53
zbMATH DE Number: 7348213
zbMATH Keywords: uniformly convex spaces
zbMATH Keywords: uniformly smooth spaces
zbMATH Keywords: generalized proximal normal cone
zbMATH Keywords: \(V\)-uniformly generalized prox-regularity
zbMATH Keywords: nonconvex sweeping process
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7348213