## Abstract

Consider a Stefan-like problem with Gibbs-Thomson and kinetic effects as a model of crystal growth from vapor. The equilibrium shape is assumed to be a
regular circular cylinder.
Our main concern is a problem whether or not a surface of cylindrical crystals
(called a facet) is stable under evolution in the sense that its normal velocity is constant over the facet.
If a facet is unstable, then it breaks or bends. A typical result we establish is that all facets are stable if the evolving crystal is near the equilibrium.
The stability criterion we use is a variational principle for selecting the correct
Cahn-Hoffman vector. The analysis of the phase plane of an evolving cylinder (identified with points in the plane) near the unique equilibrium provides a bound for ratio of velocities of top and lateral facets of the cylinders.