2002 Quasi-static evolution of 3-D crystals grown from supersaturated vapor
Y. Giga, P. Rybka
Differential Integral Equations 15(1): 1-15 (2002). DOI: 10.57262/die/1356060879

Abstract

Gonda and Gomi (T.Gonda, H.Gomi, Ann. Glaciology, 6 (1985), 222--224) have grown large elongated ice crystals from supersaturated vapor. Theoretically this problem may be recast in a framework similar to that used by Seeger (A.Seeger, Philos. Mag., ser. 7, 44, no 348, (1953) 1--13) for studies of planar crystals. The resulting set of equations is of Stefan type. We also include the Gibbs-Thomson relation on the crystal surface. In order to make this system tractable mathematically we assume that the Wulff crystal is a fixed cylinder. Subsequently we study a weak form of our system. We show local in time existence of solutions assuming that the initial shape is an arbitrary cylinder. We comment on properties of weak solutions.

Citation

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Y. Giga. P. Rybka. "Quasi-static evolution of 3-D crystals grown from supersaturated vapor." Differential Integral Equations 15 (1) 1 - 15, 2002. https://doi.org/10.57262/die/1356060879

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1038.35176
MathSciNet: MR1869818
Digital Object Identifier: 10.57262/die/1356060879

Subjects:
Primary: 35R35
Secondary: 53C44 , 80A22 , 86A40

Rights: Copyright © 2002 Khayyam Publishing, Inc.

Vol.15 • No. 1 • 2002
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