Critical size of crystals in the plane

Gorka, Przemyslaw

doi:10.4171/IFB/115

Interfaces and Free Boundaries

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Volume 7, Issue 1, 2005, pp. 99–105

DOI: 10.4171/IFB/115

Critical size of crystals in the plane

Przemyslaw Gorka (1)

(1) Department of Mathematics and Information Sciences, Technical University, Pl. Politechniki 1, 00-668, WARSZAWA, POLAND

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.

Keywords: Stefan problem, free boundary, Gibbs-Thompson law, ice ball melting