Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity.
type: Item
instance of: scholarly article
title: Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity.
zbMATH Open document ID: 1099.74051
author: Olaf Klein
published in: Applications of Mathematics
publication date: 2006-11-21T00:00:00Z
full work available at URL: https://eudml.org/doc/33187
full work available at URL: http://hdl.handle.net/10338.dmlcz/134571
review text: The author considers a system of partial differential equations in one space dimension, describing the balances of momentum and internal energy coupled with a differential phase dynamics equation, with the intention to characterize the long time evolution of a thermo-visco-elasto-plastic wire under the influence of a solid-solid phase transition in the material. Hysteresis effects in both the plastic constitutive law and in the phase transition are taken into account. In addition to a generalization of existence, uniqueness, and thermodynamic consistency results obtained in \textit{P.\ Krejčí, J.\ Sprekels} and \textit{U.\ Stefanelli} [SIAM J.\ Math.\ Anal.\ 34, 409-434 (2002; Zbl 1034.34053)], a careful estimation technique based on energy dissipation properties of hysteresis operators is used here to prove under weaker assumptions new results on asymptotic stability as time tends to infinity.
Mathematics Subject Classification ID: 74N30
Mathematics Subject Classification ID: 74N20
Mathematics Subject Classification ID: 74H40
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 5074726
zbMATH Keywords: phase transition
zbMATH Keywords: long-time behaviour
zbMATH Keywords: energy dissipation
reviewed by: Pavel Krejč{í }
MaRDI profile type: Publication
OpenAlex ID: W2068340758
cites work: On the existence of solutions to the equation \(u_{tt}=u_{xxt}+\sigma (u_x)_x\)
cites work: Hysteresis and phase transitions
cites work: Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity
cites work: Hysteresis in phase-field models with thermal memory
cites work: Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations.
cites work: Q3543379
cites work: On a system of nonlinear PDEs with temperature-dependent hysteresis in one-dimensional thermoplasticity
cites work: Hysteresis operators in phase-field models of Penrose-fife type
cites work: Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity
cites work: A hysteresis approach to phase-field models
cites work: Phase-field models with hysteresis
cites work: Q4513912
cites work: Phase‐field systems for multi‐dimensional Prandtl–Ishlinskii operators with non‐polyhedral characteristics
cites work: Q4814040
cites work: Phase-Field Models with Hysteresis in One-Dimensional Thermoviscoplasticity
cites work: Q4513823
cites work: Asymptotic behaviour for a phase-field system with hysteresis
cites work: Resonance in Preisach systems
cites work: Phase transitions in one-dimensional nonlinear viscoelasticity: Admissibility and stability
cites work: Global existence and asymptotic behavior in nonlinear thermoviscoelasticity
cites work: On The Coupled Cahn-hilliard Equations
cites work: Asymptotic Behavior of the Solutions to a Landau--Ginzburg System with Viscosity for Martensitic Phase Transitions in Shape Memory Alloys
cites work: Symmetric model of stress-strain hysteresis loops in shape memory alloys
cites work: Q4853970
DOI: 10.1007/S10492-004-6402-1
description: scientific article; zbMATH DE number 5074726