Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys
type: Item
instance of: scholarly article
title: Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys
zbMATH Open document ID: 0944.35104
DOI: 10.1016/S0167-2789(98)00167-5
author: Songmu Zheng
author: Jürgen Sprekels
published in: Physica D
publication date: 1999-12-06T00:00:00Z
review text: In this paper, a system of nonlinear partial differential equations which arises from the study of dynamics of phase transitions in shape memory alloys is treated. In a previous paper [SIAM J. Math. Anal. 29, No. 1, 69-84 (1998; Zbl 0914.35141)], it has been proved that for any given initial data with positive initial temperature, satisfying a compatibility condition, the system analysed admits a unique global solution, and, as the time tends to infinity, the solution converges to a stationary solution. In the present paper, the authors further investigate the dynamics defined by the analysed system of nonlinear partial differential equations with linear initial and boundary conditions. They prove the existence of a compact maximal attractor.
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 74N30
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1374382
zbMATH Keywords: martensitic phase transitions
zbMATH Keywords: orbits
zbMATH Keywords: Landau-Ginzburg theory
zbMATH Keywords: nonlinear thermoviscoelasticity
zbMATH Keywords: shape memory allows
zbMATH Keywords: compact attractor
reviewed by: István Ecsedi
MaRDI profile type: Publication
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full work available at URL: s0167-2789(98)00167-5
OpenAlex ID: W2095445455
description: scientific article; zbMATH DE number 1374382