Stability for a phase field model with the total variation functional as the interfacial energy Original Research Article

In this paper, we treat a one-dimensional solid–liquid phase transition model in which the interface energy is given by the total variation functional of the order parameter. We discuss the large time behavior of solutions of our problem under such a condition on initial data that the initial temperature is uniformly close to the phase transition temperature and the initial state of the material is sufficiently close to a class of steady states.