Periodic solutions of the Stefan problem with hysteresis-type boundary conditions (Q1313539)

The authors consider the problem that in a two-phase Stefan problem in one-dimensional geometry the free boundary is controlled by the actions of a thermostat relay controlling the heat flux over the lateral boundaries of the system. In this way an automatic feedback is realized which, owing to the hysteretic nature of the relay, keeps track of the past evolution of the system. The main result of the paper is that, under suitable conditions for the parameters defining the system, periodic solutions exist.