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Zbl 0608.35080
Caginalp, Gunduz
An analysis of a phase field model of a free boundary. (English)
[J] Arch. Ration. Mech. Anal. 92, 205-245 (1986). ISSN 0003-9527; ISSN 1432-0673/e

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.
[J.Sprekels]

MSC 2000:: *35R35 Free boundary problems for PDE
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

Cited in: Zbl pre06097429 Zbl pre06160815 Zbl 1103.65140 Zbl 1063.35038 Zbl 1043.35086 Zbl 0922.35191 Zbl 0859.65103 Zbl 1027.35139 Zbl 0804.35063 Zbl 0835.35158 Zbl 0768.93070 Zbl 0754.35190 Zbl 0753.35125 Zbl 0709.76001 Zbl 0681.49012 Zbl 0663.35098

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