WIAS Preprint No. 214, (1996)

Asymptotic Behavior of the Solutions to a Landau-Ginzburg System with Viscosity for Martensitic Phase Transitions in Shape Memory Alloys


Authors

  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604
  • Zheng, Songmu
  • Zhu, Peicheng

2010 Mathematics Subject Classification

  • 35Q72 73B30 35B40

Keywords

  • Nonlinear thermoviscoelasticity, shape memory alloys, phase transitions asymptotic behaviour, compact orbits, Landau-Ginzburg theory

DOI

10.20347/WIAS.PREPRINT.214

Abstract

In this paper, we investigate the system of partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys under the presence of a (possibly small) viscous stress. The corresponding free energy is assumed in Landau-Ginzburg form and nonconvex as function of the order parameter. Results concerning the asymptotic behavior of the solution as time tends to infinity are proved, and the compactness of the orbit is shown.

Appeared in

  • SIAM J. Math. Anal. 29 (1998) pp. 69 - 84

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