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

Abstract

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 ) , i.e., q = 0 on the boundary, where θ > 0 is the temperature. There is a unique H 1 solution globally in time with the non-empty, connected, compact ω -limit set composed of stationary solutions, and the linearized stable stationary solution is dynamically stable.