Phase-Field Model with Temperature Dependent Constraint1

This paper is concerned with a phase-field model with temperature dependent constraint for the order parameter. In the kinetic equation of the order parameter, we take account of diffusion as well as the undercooled/superheated state which is modelled by means of a hysteresis input–output relation; the input is the temperature field and the output is the order parameter. In this paper we shall show that there exists a solution “globally” in time in a physically reasonable sense, when the coefficient of interfacial energy is sufficiently small