Global Solutions to a Penrose–Fife Phase-field Model Under Flux Boundary Conditions for the Inverse Temperature

In this paper, we study an initial-boundary value problem for a system of phase-field equations arising from the Penrose–Fife approach to model the kinetics of phase transitions. In contrast to other recent works in the field, the correct form of the boundary condition for the temperature field is assumed which leads to additional difficulties in the mathematical treatment. It is demonstrated that global existence of strong solutions can be shown under essentially the same assumptions on the data as in the previous papers where a simplified boundary condition for the heat exchange with the surrounding medium has been used.