  In this paper we derive, starting from the basic principles of
Thermodynamics, an extended version of the nonconserved Penrose-Fife phase
transition model, in which dynamic boundary conditions are considered in order
to take into account interactions with walls. Moreover, we study the
well-posedness and the asymptotic behavior of the Cauchy problem for the PDE
system associated to the model, allowing the phase configuration of the
material to be described by a singular function.
