Critical size of crystals in the plane

Abstract

We study a modified Stefan problem (and its quasi-steady approximation) of crystalline motion in the plane. We are interested in behaviour of solution for a symmetric problem, in particular we assume that Wulff shape $W$ is a regular polygon with $N$ sides. We describe two situations. In the first situation we show that ice will be melting. In the second one we examine properties of $V(t)$ for small $t$ assuming that $V(0)=0$, where $V$ is a velocity of the interfacial curve.