Global existence and asymptotic behaviour for a nonlocal phase-field model for non-isothermal phase transitions
- Sprekels, Jürgen
- Zheng, Songmu
2010 Mathematics Subject Classification
- 35B40 35K50 45J05 45K05
- Phase transitions, nonlocal models, initial-boundary value problems, a priori estimates, asymptotic behaviour, well-posedness, integrodifferential equations
In this paper a nonlocal phase-field model for non-isothermal phase transitions with a non-conserved 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. Krejčí and the authors for phase-field systems involving hysteresis operators.
- J. Math. Anal. Appl., 279 (2003), pp. 97-110