A characterization of energetic and \(BV\) solutions to one-dimensional rate-independent systems
type: Item
instance of: scholarly article
title: A characterization of energetic and \(BV\) solutions to one-dimensional rate-independent systems
zbMATH Open document ID: 1270.34027
author: Riccarda Rossi
author: Giuseppe Savaré
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2013-03-14T00:00:00Z
review text: The authors obtain a characterization of BV solutions and energetic solutions to rate-independent systems in the one-dimensional setting: \[ 0\in \partial \psi(u'(t)) + D \mathcal{E}_t(u(t)) \quad \text{in \(\mathbb{R}\), for a.e. \(t \in (0,T)\);} \] where \(\psi\) is a dissipation potential and the energy functional \(\mathcal{E}\) has the form \(\mathcal{E}_t(u) = W(u)-l(t)u\). Moreover, an explicit characterization of such solutions is given in the case when the loading \(l\) is monotone.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C55
Mathematics Subject Classification ID: 47J20
zbMATH DE Number: 6144712
zbMATH Keywords: abstract evolution equations
zbMATH Keywords: rate-independent systems
zbMATH Keywords: energetic and BV solutions
zbMATH Keywords: hysteresis effects
reviewed by: Marlène Frigon
MaRDI profile type: Publication
full work available at URL: dcdss.2013.6.167
OpenAlex ID: W2317700653
DOI: 10.3934/DCDSS.2013.6.167
description: scientific article; zbMATH DE number 6144712