The Conserved Penrose-Fife Phase Field Model with Special Heat Flux Laws and Memory Effects
Elisabetta Rocca · Journal of Integral Equations and Applications · 2002
In 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.