On a Penrose-Fife type system with Dirichlet boundary conditions for temperature

We deal with the Dirichlet problem for a class of Penrose-Fife phase field models for phase transitions, An existence result is obtained by approximating the non-homogeneous Dirichlet condition with classical third type conditions on the heat flux at the boundary of the domain where the model is considered. Moreover, we prove a regularity and uniqueness result under stronger assumptions on the regularity of the data. Suitable assumptions on the behaviour of the heat flux at zero and infinity are considered.