Global stability and decay for the classical Stefan problem

Mahir Hadzic, Steve Shkoller

Research output: Working paper/PreprintPreprint

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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.
Original languageEnglish
Number of pages50
Publication statusPublished - 6 Dec 2012


  • math.AP
  • 35R35, 35B65, 35K05, 80A22


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