Weak Solution to Some Penrose–Fife Phase-Field Systems with Temperature-Dependent Memory

In this paper a phase-field model of Penrose–Fife type is considered for a diffusive phase transition in a material in which the heat flux is a superposition of two different contributions: one part is proportional to the spatial gradient of the inverse temperature, while the other is of the form of the Gurtin–Pipkin law introduced in the theory of materials with thermal memory. It is shown that an initial-boundary value problem for the resulting state equations has a unique solution, thereby generalizing a number of recent results.