Regularization of nonconvex sweeping process in Hilbert space
type: Item
instance of: scholarly article
title: Regularization of nonconvex sweeping process in Hilbert space
zbMATH Open document ID: 1162.34010
author: L. Thibault
published in: Set-Valued Analysis
publication date: 2008-06-25T00:00:00Z
review text: This paper is concerned with the of solution for the follwing sweeping process \[ u'(t)\in -N_{C(t)}(u(t)), \] \[ u(T_0)=a\in C(T_0), \] where \([T_0,T)\) is an interval of \(\mathbb R,\) \(C(t)\) is a closed subset of a Hilbert space \(H\) for each \(t\in[T_0,T],\) and \(u(T_0)=a\) is the initial condition. Under the Lipschitzian variation of the set-valued mapping \(C(.)\) and under the prox-regularity assumption of \(C(.),\) the author proves the existence and uniqueness of a solution to the problem above.
reviewed by: Abdelghani Ouahab
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49J24
Mathematics Subject Classification ID: 49J53
zbMATH DE Number: 5292866
zbMATH Keywords: Moreau's sweeping process
zbMATH Keywords: normal cone
zbMATH Keywords: differential inclusion regularization
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: prox-regular set
MaRDI profile type: Publication
full work available at URL: s11228-008-0083-y
OpenAlex ID: W1968736803
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DOI: 10.1007/S11228-008-0083-Y
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description: scientific article; zbMATH DE number 5292866