Asymptotic hysteresis patterns in a phase separation problem

Abstract

A non-smooth temperature-driven phase separation model with conserved energy and a large set of equilibria is shown to develop spontaneously two different time scales as time tends to infinity. The temperature evolution becomes slower and slower, while the microevolution on the unknown phase interface keeps its own independent characteristic speed. In the large time limit, the temperature becomes 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.