Asymptotic Behaviour for a Phase-Field System with Hysteresis

The method of hysteresis operators in modelling phase transitions is applied here to the problem of asymptotic stabilization of solutions to a phase-field system with hysteresis. While it is known that a unique global strong solution exists for every initial data and that the evolution process described by this system is thermo-dynamically consistent in the sense that the absolute temperature remains positive for all times and the Clausius–Duhem inequality holds almost everywhere, we study here the asymptotic behaviour of the solution as t→∞.