Asymptotic behavior of the solution to the non-isothermal phase field equation Original Research Article

We consider the Penrose–Fife phase field model [Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D 43 (1990) 44–62] with homogeneous Neumann boundary condition to the nonlinear heat flux q=∇(1/θ)q=∇(1/θ), i.e., q=0q=0 on the boundary, where θ>0θ>0 is the temperature. There is a unique H1H1 solution globally in time with the non-empty, connected, compact ωω-limit set composed of stationary solutions, and the linearized stable stationary solution is dynamically stable.