The aim of this paper is to analyze the well posedness of the one-phase quasi-stationary Stefan problem with the Gibbs-Thomson correction in a two-dimensional domain which is a perturbation of the half plane. We show the existence of a unique regular solution for an arbitrary time interval, under suitable smallness assumptions on initial data. The existence is shown in the Besov-Slobodetskiĭ class with sharp regularity in the L₂-framework.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-14,
author = {Piotr Bogus\l aw Mucha},
title = {Stefan problem in a 2D case},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {149-165},
zbl = {1099.35179},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-14}
}
Piotr Bogusław Mucha. Stefan problem in a 2D case. Colloquium Mathematicae, Tome 106 (2006) pp. 149-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-14/