A hysteresis approach to phase-field models
type: Item
instance of: scholarly article
title: A hysteresis approach to phase-field models
zbMATH Open document ID: 0941.35123
DOI: 10.1016/S0362-546X(98)00222-3
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-11-19T00:00:00Z
review text: The phase-field model is described by a system of equations for an order parameter \(w\) and the absolute temperature \(T\) involving hysteresis operators, that is to say, loosely speaking, functions of sets. The differential inclusion is converted into an inequality, the solution of which is defined as a set function. Uniqueness and existence theorems are stated, the solution is constructed by a successive approximation, and its stability is analyzed. There is thermodynamic consistency.
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 74N30
Mathematics Subject Classification ID: 82C26
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1389678
zbMATH Keywords: uniqueness
zbMATH Keywords: phase-field model
zbMATH Keywords: hysteresis operators
zbMATH Keywords: approximation
zbMATH Keywords: stability
zbMATH Keywords: thermodynamic consistency
author: Pavel Krejč{í }
author: Jürgen Sprekels
reviewed by: Guy Jumarie
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1389678