English

Global stability of steady states in the classical Stefan problem

Analysis of PDEs 2015-01-05 v1

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.

Keywords

Cite

@article{arxiv.1501.00463,
  title  = {Global stability of steady states in the classical Stefan problem},
  author = {Mahir Hadžić and Steve Shkoller},
  journal= {arXiv preprint arXiv:1501.00463},
  year   = {2015}
}

Comments

14 pages. arXiv admin note: substantial text overlap with arXiv:1212.1422