Nonlinear systems describing phase transition models compatible with thermodynamics

This paper is devoted to analyzing solutions of a nonlinear evolution syste m describing the phase transition in a rigid heat conductor in the presence of phase relaxation. First, in a general framework, a rate type constituti ve law for the phase variable is considered and matched with the Helmholtz free energy involving the state of the material. Thermodynamic compatibilit y of the resulting models is scrutinized. Moreover, a comparison with a dif ferent phase change modelling is performed. Under proper assumptions, a non linear system in the (absolute) temperature and phase variable is achieved. For it, existence and uniqueness of the solution is proved and positivity of temperature is recovered.