The conserved Penrose--Fife system with Fourier heat flux law. (Q1395845)

The Penrose-Fife system is a model for phase transitions and describes the space-time evolution of the absolute temperature \(\vartheta>0\) and the order parameter \(\chi\) (which is the state variable characterizing the phase). In its conserved version, it couples a second-order parabolic equation for \(\vartheta\) to a fourth-order parabolic equation for \(\chi\) (the latter being similar to the Cahn-Hilliard equation). Existence of a weak solution to this system is proved by a compactness method when the heat flux \({\mathbf q} = - k \nabla \vartheta\) is given by the Fourier law, the latent heat is constant, and the boundary conditions are homogeneous Neumann boundary conditions.