Advances in Differential Equations

Stability of facets of self-similar motion of a crystal

Yoshikazu Giga and Piotr Rybka

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Giga, Yoshikazu; Rybka, Piotr. Stability of facets of self-similar motion of a crystal. Adv. Differential Equations 10 (2005), no. 6, 601--634.

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