Non-isothermal phase transition models with Neumann boundary conditions.
The Penrose-Fife system is a model of phase transitions which describes the space-time evolution of the absolute temperature \(u>0\) and the order parameter \(w\) (which is the state variable characterizing the phase). This system couples a second-order parabolic equation for \(u\) to a second-order (non-conserved case) or a fourth-order (conserved case) parabolic variational inequality for \(w\). For the heat flux \(\mathbf{q}=\nabla(1/u)\), several existence and uniqueness results have already been obtained for the mixed boundary condition \(\partial_\nu(1/u) + n_0 (1/u) = 0\) for the inverse temperature \(1/u\) with \(n_0>0\). These results are extended here to homogeneous Neumann boundary conditions \(\partial_\nu(1/u)=0\) (\(n_0=0\)) for the inverse temperature.
scientific article; zbMATH DE number 1945015