A non-isothermal phase separation with constraints and Dirichlet boundary condition for temperature Original Research Article

We consider non-isothermal phase separation models of the Penrose–Fife type, which were proposed in [O. Penrose, P.C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D 43 (1990) 44–62]. In the present paper, we impose a non-homogeneous Dirichlet boundary condition on the nonlinear heat flux. Moreover, we consider two cases as boundary conditions for the conserved order parameter. One is the homogeneous Neumann boundary condition and the other is the Signorini boundary condition, which is nonlinear. We show the existence and uniqueness of solutions to these models.