Existence of solutions to the nonconvex sweeping process
type: Item
instance of: scholarly article
title: Existence of solutions to the nonconvex sweeping process
zbMATH Open document ID: 0957.34061
author: H. Benabdellah
published in: Journal of Differential Equations
publication date: 2001-04-01T00:00:00Z
review text: In this paper, the author proves the existence of solutions to the sweeping process problem \[ x'(t)\in-N_{C(t)} \bigl(x(t) \bigr)\text{ a.e. }, x(t)\in C(t),\;x(0)=x_0\in C(0), \] where \(C(\cdot)\) is an arbitrary Hausdorff-Lipschitzian multifunction from \(I=[0,T]\) onto the set of nonempty closed subsets of \(\mathbb{R}^d\). This generalizes a well-known result of \textit{J. J. Moreau} [Rafle par un convexe variable. I. Trav. Sémin. d'Anal. convexe, Montpellier, Vol. 1, Exposé No. 15 (1971; Zbl 0343.49019)].
reviewed by: Stanisław Wedrychowicz
Mathematics Subject Classification ID: 34G25
zbMATH DE Number: 1515444
zbMATH Keywords: existence
zbMATH Keywords: solutions
zbMATH Keywords: sweeping process problem
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3756
OpenAlex ID: W2063311431
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DOI: 10.1006/JDEQ.1999.3756
description: scientific article; zbMATH DE number 1515444