Global stability of steady states in the classical Stefan problem
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Global stability of steady states in the classical Stefan problem

  • Author(s): Hadžić, Mahir
  • Shkoller, Steve
  • et al.

Published Web Location

https://arxiv.org/pdf/1501.00463.pdf
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Abstract

The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of such steady states, assuming a sufficient degree of smoothness on the initial domain, but without any a priori restriction on the convexity properties of the initial shape. This is an extension of our previous result [28] in which we studied nearly spherical shapes.

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