Maximal Attractor for the System of a Landau-Ginzburg Theory for Structural Phase Transitions in Shape Memory Alloys
- Sprekels, Jürgen
- Zheng, Songmu
2010 Mathematics Subject Classification
- 35Q72 73B30 35B40
- Maximal attractors, shape memory alloys, asymptotic behavior, phase transitions, nonlinear systems of PDEs
In this paper, a system of partial differential equations modelling the dynamics of martensitic phase transitions in shape memory alloys is further investigated. In this system, the free energy is assumed to be in the Landau-Ginzburg form and nonconvex in the order parameter; the materials are assumed to be viscous. In a previous paper published in SIAM J. Math. Anal. the global existence of a unique solution and the compactness of the orbit have been established; in the present paper the existence of a compact maximal attractor is proved.
- Physica D 121, pp. 252-262