Stefan problem in a 2D case
Volume 105 / 2006
Colloquium Mathematicum 105 (2006), 149-165
MSC: 35R35, 35K99.
DOI: 10.4064/cm105-1-14
Abstract
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–Slobodetski{ĭ} class with sharp regularity in the $L_2$-framework.
