On the melting of ice balls

Abstract

We consider here the problem of describing the melting of an ice ball surrounded by water. The corresponding mathematical model consists of the Stefan problem with radial symmetry. We obtain asymptotic expansions for the radius of the melting ball which turn out to be of a different nature according to the cases N greater than or equal to 3 and N = 2, N being the space dimension. The methods employed combine matched asymptotic expansion techniques, a priori estimates, and topological results.