A quasi-stationary phase field model with micro-movements

This note addresses the global strong solvability of a phase-field system arising in connection with the phase transition theory recently proposed by Frémond. The novelty of this modelization consists in considering the macroscopic effect of the microscopic movements of particles of the system that undergoes the phase transition. In particular, we outline the basic features of this model and deal with the upcoming nonlinear PDE system in the one-dimensional setting by means of an approximation—a priori estimates—passage to the limit procedure.