Hyperbolic Phase-Field Dynamics with Memory

We consider a non-conserved phase-field system which consists of two nonlinearly coupled hyperbolic integrodifferential equations. This model is derived from two basic assumptions: the heat flux law is of Gurtin–Pipkin type and the response of the order parameter to the variation of the free energy functional is delayed. These hypotheses might be a reasonable attempt to describe, for instance, the melt of He4 crystals. A suitable initial and boundary value problem is then associated with the system and its well-posedness is analyzed in detail.