An analysis of a phase field model of a free boundary. (English) Zbl 0608.35080

Caginalp, Gunduz

Arch. Ration. Mech. Anal. 92, 205-245 (1986).

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

MSC:

35R35	Free boundary problems for PDEs
35K55	Nonlinear parabolic equations

Keywords:

solidification problems; phase transition; nonlinearly coupled parabolic system; global existence; unique solution; invariant regions; regularity; Gibbs-Thompson condition; surface tension; curvature

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