On a decay rate for a Landau-Ginzburg system with viscosity for martensitic phase transitions in shape memory alloys
- Vodák, Rostislav
2010 Mathematics Subject Classification
- 35Q72 73B30 35B40
- nonlinear thermo-viscoelasticity, shape memory alloys, phase transitions, asymptotic behaviour, Landau-Ginzburg theory
In this paper, we investigate the decay rate of stabilization of the solution of the system of partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys under the presence of a viscous stress. The corresponding free energy is assumed in Landau-Ginzburg form and nonconvex as a function of the order parametr. We prove that for appropriate constants, which appear in the above-mentioned model, we can decide upon the exponencial decrease of the solution to its attractor for time tending to infinity.
- Adv. Math. Sci. Appl. 14 (2004), no. 1, 295--305.