Advances in Differential Equations

Stability of facets of self-similar motion of a crystal

Yoshikazu Giga and Piotr Rybka

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Abstract

We are concerned with a quasi-steady Stefan type problem with Gibbs-Thomson relation and the mobility term which is a model for a crystal growing from supersaturated vapor. The evolving crystal and the Wulff shape of the interfacial energy are assumed to be (right-circular) cylinders. In pattern formation deciding what are the conditions which guarantee that the speed in the normal direction is constant over each facet, so that the facet does not break, is an important question. We formulate such a condition with the aid of a convex variational problem with a convex obstacle type constraint. We derive necessary and sufficient conditions for the nonbreaking of facets in terms of the size and the supersaturation at space infinity when the motion is self-similar.

Article information

Source
Adv. Differential Equations Volume 10, Number 6 (2005), 601-634.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867837

Mathematical Reviews number (MathSciNet)
MR2133647

Zentralblatt MATH identifier
1109.35122

Subjects
Primary: 35R35: Free boundary problems
Secondary: 74N05: Crystals 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]

Citation

Giga, Yoshikazu; Rybka, Piotr. Stability of facets of self-similar motion of a crystal. Adv. Differential Equations 10 (2005), no. 6, 601--634. https://projecteuclid.org/euclid.ade/1355867837.


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