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

In this paper a nonlocal phase-field model for non-isothermal phase transitions with a nonconserved order parameter is studied. The paper extends recent investigations to the non-isothermal situation, complementing results obtained by 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 asymptotic behaviour are derived. The main results are proved using techniques that have been recently developed by P. Krejˇcí and the authors for phase-field systems involving hysteresis operators.  2003 Elsevier Science (USA). All rights reserved