Global stability and decay for the classical Stefan problem

2012/12/06 by Hadžić, Mahir, Shkoller, Steve · 1 citation
#35B65 #35K05 #35R35 #80A22 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/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.

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• An inverse problem for the one-phase Stefan problem with varying melting temperature

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