Unbounded state-dependent sweeping processes with perturbations in uniformly convex and \(q\)-uniformly smooth Banach spaces
type: Item
instance of: scholarly article
title: Unbounded state-dependent sweeping processes with perturbations in uniformly convex and \(q\)-uniformly smooth Banach spaces
zbMATH Open document ID: 1417.34048
author: Samir Adly
author: Ba Khiet Le
published in: Numerical Algebra, Control and Optimization
publication date: 2019-01-24T00:00:00Z
review text: Let \(X\) be a uniformly convex and \(q\)-uniformly smooth Banach space \((q\geq 2)\), \(X^*\) its dual space, \(J, J^*\) their duality mappings. \par The authors study the existence of solutions of the following problem \[ (y^*)'(t) \in - N_{C(t,J^*y^*(t))}(J^*y^*(t))-F(t,J^*y^*(t)) \; \text{a.e. } \; t\in [0, 1], \] \[ y^*(0) = J y_0, y_0\in C(0,y_0), \] where \(C:[0,T]\times X\multimap X\) with convex closed values satisfies Lipschitz type conditions, and the perturbation \(F:[0,T]\times X\multimap X^*\) is upper semicontinuous with convex weak\(^*\) compact values with linear growth conditions, \(N_C\) denotes outward normal cone. This may be seen as a sweeping process with a perturbation. Similar second-order problems are considered. \par Proofs use suitable modifications of Moreau' catching up algorithm.
reviewed by: Zdzisław Dzedzej
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 49J53
zbMATH DE Number: 7006498
zbMATH Keywords: unbounded state-dependent sweeping processes
zbMATH Keywords: differential inclusions
zbMATH Keywords: normal cones
zbMATH Keywords: variational analysis
zbMATH Keywords: uniformly convex and \(q\)-uniformly smooth Banach space
MaRDI profile type: Publication
full work available at URL: naco.2018005
OpenAlex ID: W2792307189
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DOI: 10.3934/NACO.2018005
description: scientific article; zbMATH DE number 7006498