Maximal attractor for the system of a Landau-Ginzburg theory for structural phase transitions in shape memory alloys
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.
scientific article; zbMATH DE number 1374382