EXISTENCE OF WEAK SOLUTIONS FORTHE STEFAN PROBLEM WITHANISOTROPIC GIBBS-THOMSON LAW

摘要

The Stefan problem with Gibbs-Thomson law describes solidification phenomena for pure substances. In applications the surface energy is anisotropic leading to an anisotropic Gibbs-Thomson law. We show the existence of weak solu-tions to the Stefan problem with anisotropic Gibbs-Thomson law using an implicit time discretization, and variational methods in an anisotropic BV setting. Our main result generalizes an existence result of Luckhaus to the anisotropic case.