Hyperbolic phase-field dynamics with memory

We consider a non-conserved phase-field system which consists of two nonlin early coupled hyperbolic integrodifferential equations. This model is deriv ed from two basic assumptions: the heat flux law is of Gurtin-Pipkin type a nd the response of the order parameter to the variation of the free energy functional is delayed. These hypotheses might be a reasonable attempt to de scribe, for instance, the melt of He-4 crystals. A suitable initial and bou ndary value problem is then associated with the system and its well-posedne ss is analyzed in detail. (C) 2001 Academic Press.