Well-posedness and longtime behavior of the phase-field model with memory in a history space setting

Authors:
Claudio Giorgi, Maurizio Grasselli and Vittorino Pata

Journal:
Quart. Appl. Math. **59** (2001), 701-736

MSC:
Primary 45K05; Secondary 35B30, 35B40

DOI:
https://doi.org/10.1090/qam/1866554

MathSciNet review:
MR1866554

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Abstract | References | Similar Articles | Additional Information

Abstract: A thermodynamically consistent phase-field model with memory, based on the linearized version of the Gurtin-Pipkin heat conduction law, is considered. The formulation of an initial and boundary value problem for the phase-field evolution system is framed in a history space setting. Namely, the summed past history of the temperature is regarded itself as a variable along with the temperature and the phase-field. Well-posedness results are discussed, as well as longtime behavior of solutions. Under suitable conditions, the existence of an absorbing set can be achieved.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1866554

Article copyright:
© Copyright 2001
American Mathematical Society