On phase-field equations of Penrose-Fife type with non-conserved order parameter under flux boundary condition. II: Uniform boundedness

In [1] we showed the global-in-time solvability of the initial-boundary value problem for the non-conserved phase-field model proposed by Penrose and Fife [2, 3] under the correct form of flux boundary condition for the temperature field in higher space dimensions. In this paper we discuss the uniform boundedness up to the infinite time of its solution in Sobolev-Slobodetskiĭ spaces.