In the present paper we consider a partial differential system describing a phase-field model with temperature dependent constraint for the order parameter. The system consists of an energy balance equation with a fairly general nonlinear heat source term and a phase dynamics equation which takes into account the hysteretic character of the process. The existence of a periodic solution for this system is proved under a minimal set of assumptions on the curves defining the corresponding hysteresis region.
@article{arxiv.2001.04149,
title = {Periodic solutions of a phase-field model with hysteresis},
author = {Chen Bin and Sergey A. Timoshin},
journal= {arXiv preprint arXiv:2001.04149},
year = {2021}
}