Pointwise asymptotic convergence of solutions for a phase separation model

Abstract

A new technique, combining the global energy and entropy balance equations with the local stability theory for dynamical systems, is used for proving that every solution to a non-smooth temperature-driven phase separation model with conserved energy converges pointwise in space to an equilibrium as time tends to infinity. Three main features are observed: the limit temperature is uniform in space, there exists a partition of the physical body into at most three constant limit phases, and the phase separation process has a hysteresis-like character.