Global stability and decay for the classical Stefan problem
arXiv:1212.1422
Abstract
The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain whose boundary is transported by the normal derivative of the temperature along the evolving and a priori unknown free-boundary. We establish a global-in-time stability result for nearly spherical geometries and small temperatures, using a novel hybrid methodology, which combines energy estimates, decay estimates, and Hopf-type inequalities.
50 pages, references added, minor typos corrected, to appear in Comm. Pure Appl. Math, abstract added for UK REF