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An analysis of a phase field model of a free boundary. (English) Zbl 0608.35080
The paper presents a new approach to solidification problems by assuming that the free boundary arising from a phase transition is not a sharp interface but has finite thickness. Assuming a free energy of Landau- Ginzburg from and relaxation-type dynamics, the author constructs a nonlinearly coupled parabolic system for temperature and phase function as mathematical model. The global existence of a unique solution is proved by constructing invariant regions for the system, and regularity results of Schauder type are obtained. An asymptotic analysis leads to the Gibbs-Thompson condition which relates the temperature at the interface to the surface tension and curvature.
Reviewer: J.Sprekels

35R35Free boundary problems for PDE
35K55Nonlinear parabolic equations
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