  In this paper we analyze a class of phase field models for the dynamics of
phase transitions which extend the well-known Caginalp and Penrose-Fife models.
Existence and uniqueness of the solution to the related initial boundary value
problem are shown. Further regularity of the solution is deduced by exploiting
the so-called regularizing effect. Then, the large time behavior of such a
solution is studied and several convergence properties of the trajectory as
time tends to infinity are discussed.
