FACETED CRYSTALS GROWN FROM SOLUTION - A STEFAN TYPE PROBLEM WITH A SINGULAR INTERFACIAL ENERGY

We present a one-phase quasi-steady Stefan problem with Gibbs-Thomson and the kinetic effects when the interfacial energy is singular so that the equilibrium shape is a cylinder. We derive this model to describe crystal growth from vapor or solution. We summarize mathematical results on this model. Among other results we prove that a cylindrical shape is preserved if the initial cylindrical shape of a crystal is close to the equilibrium shape. Our formulation allows the possibility that cylindrical shape may break