Stability of facets of self-similar motion of a crystal
Preprint Series # 636
Giga, Yoshikazu and Rybka, Piotr Stability of facets of self-similar motion of a crystal. (2004);
We are concerned with a quasi-steady Stefan type
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 an aid of a convex variational
problem with a convex obstacle type constraint.
sufficient conditions for the non-breaking of facets in terms of the
size and the supersaturation at space infinity when the motion is