Global existence and asymptotic behaviour for a nonlocal phase-field model for non-isothermal phase transitions (Q1874578)

In this paper a nonlocal phase-field model for non-isothermal phase transition with a non-conserved order parameter is studied. The paper extends recents investigastions to the non-isothermal situation, complementing results obtained H. Gajewski for the non-isothermal case for conserved order parameters in phase separation phenomena. The resulting field equations studied in this paper form a system of integro-partial differential equations which are highly nonlinearly coupled. For this system, results concerning global existence, uniqueness and large-time behavoiur are derived. The main results are proved using techniques that have been recently developed by P. K. Krejci and the authors for phase-field systems involving hysteresis operators.