On a Penrose-Fife phase-field model with nonhomogeneous Neumann boundary conditions for the temperature

Abstract

This work is concerned with the study of an initial and boundary value problem for a nonconserved system of phase field equations arising from the Penrose-Fife approach to phase transitions problems. Several works deal with variations of the same problem coupled with third type boundary conditions for the heat flux. On the contrary, our aim is to consider the case of the nonhomogeneous Neumann boundary condition for the heat flux, to find well-posedness for a weak formulation of this problem, and to prove a regularity result in case of smoother data and a slightly less general heat flux law.