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.
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