A level set method for spiral crystal growth

Abstract

In this paper we introduce a new level set model for the growth of spirals on the surface of a crystal. Since the conventional level set method cannot express a spiral curve having orientation, we modify the level set method by using a sheet structure function. Since the model equation we obtain is degenerate parabolic, we need to consider a notion of weak solution. Our goal is to prove the existence and the uniqueness of the solution for our model in the sence of viscosity solutions.