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arXiv · 1212.1422

Global stability and decay for the classical Stefan problem

Mahir Hadžić·Steve Shkoller
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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.

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Mahir Hadžić, Steve Shkoller. 2013-10-20. Global stability and decay for the classical Stefan problem. https://arxiv.org/abs/1212.1422

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