Differential and Integral Equations

Quasi-static evolution of 3-D crystals grown from supersaturated vapor

Y. Giga and P. Rybka

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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.

Article information

Differential Integral Equations, Volume 15, Number 1 (2002), 1-15.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 80A22: Stefan problems, phase changes, etc. [See also 74Nxx] 86A40: Glaciology


Giga, Y.; Rybka, P. Quasi-static evolution of 3-D crystals grown from supersaturated vapor. Differential Integral Equations 15 (2002), no. 1, 1--15. https://projecteuclid.org/euclid.die/1356060879

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