The Penrose-Fife phase-field model with coupled dynamic boundary conditions

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 initial-boundary value problem for the PDE system associated to the model, allowing the phase conguration of the material to be described by a singular function.