The conserved Penrose-Fife phase field model with special heat flux laws and memory effects

n this paper a phase-field model of Penrose-Fife type is considered for diffusive phase transitions with conserved order parameter. Different motivations lead to investigate the case when the heat flux is the superposition of two different contributions; one part is the gradient of a function of the absolute temperature θ, behaving like 1/θ as θ approaches to 0 and like -θ as θ ↗ +∞, while the other is given by the Gurtin-Pipkin law introduced in the theory of materials with thermal memory. An existence result for a related initial-boundary value problem is proven. Strengthening some assumptions on the data, the uniqueness of the solution is also achieved.