On rate-independent hysteresis models
type: Item
instance of: scholarly article
title: On rate-independent hysteresis models
zbMATH Open document ID: 1061.35182
author: Alexander Mielke
author: Florian Theil
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2004-12-16T00:00:00Z
review text: The authors develop a general approach based on energy principles for studying rate-independent processes with hysteresis. The involved energy functionals are the potential energy \(I(t,z)\) and the dissipation \(\Delta(\dot{z})\), where \(z\) is the variable describing the process and \(\dot{z}\) is the time variable, assuming that \(\Delta\) is homogeneous of degree 1 for ensuring the rate-independence. In the convex case, the authors' formulation becomes an inclusion problem in terms of subdifferential which is stated as \(0\in\partial\Delta(\dot{z})+\partial I(t,z)\). Various results for existence, uniqueness and temporal smoothness of solutions are given.
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 35K85
zbMATH DE Number: 2123247
zbMATH Keywords: variational inequality
zbMATH Keywords: hysteresis
zbMATH Keywords: energy principles
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: smoothness
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
full work available at URL: s00030-003-1052-7
OpenAlex ID: W1989046305
Wikidata QID: Q59902015
DOI: 10.1007/S00030-003-1052-7
description: scientific article; zbMATH DE number 2123247