A differential equation approach to implicit sweeping processes
type: Item
instance of: scholarly article
title: A differential equation approach to implicit sweeping processes
zbMATH Open document ID: 1433.49014
author: Abderrahim Jourani
author: E. Vilches
published in: Journal of Differential Equations
publication date: 2019-02-08T00:00:00Z
review text: In this paper, the well-posedness (existence and uniqueness of solutions) for an implicit version of the sweeping process was studied. The approach presented in this paper consists in transforming the implicit sweeping process into a differential equation for which the existence and uniqueness of solutions can be obtained through classical results of differential equationsin Hilbert spaces. Furthermore, the authors applied this equivalence to study Lyapunov pairs for the implicit sweeping process, which show the efficiency of this approach, and gave two applications of implicit sweeping processes to quasistatic evolution variational inequalities and electrical circuits, respectively. This paper improves known results in the literature.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 37L45
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 47J22
Mathematics Subject Classification ID: 58E35
zbMATH DE Number: 7018397
zbMATH Keywords: variational inequalities
zbMATH Keywords: nonlinear operators
zbMATH Keywords: sensitivity
zbMATH Keywords: stability
zbMATH Keywords: monotone operators
zbMATH Keywords: ordinary differential operators
reviewed by: Hengyou Lan
MaRDI profile type: Publication
full work available at URL: j.jde.2018.10.024
OpenAlex ID: W2896363275
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Wikidata QID: Q129044138
DOI: 10.1016/J.JDE.2018.10.024
description: scientific article; zbMATH DE number 7018397