Stefan problem in a 2D case

Piotr Bogusław Mucha. "Stefan problem in a 2D case." Colloquium Mathematicae 105.1 (2006): 149-165. <http://eudml.org/doc/284366>.

@article{PiotrBogusławMucha2006,
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-Slobodetskiĭ class with sharp regularity in the L₂-framework.},
author = {Piotr Bogusław Mucha},
journal = {Colloquium Mathematicae},
keywords = {parabolic equations of fractional order; regular solutions; Schauder-type estimates; quasi-stationary Stefan problem with the Gibbs-Thomson correction; Besov-Slobodetskiĭ class},
language = {eng},
number = {1},
pages = {149-165},
title = {Stefan problem in a 2D case},
url = {http://eudml.org/doc/284366},
volume = {105},
year = {2006},
}

TY - JOUR
AU - Piotr Bogusław Mucha
TI - Stefan problem in a 2D case
JO - Colloquium Mathematicae
PY - 2006
VL - 105
IS - 1
SP - 149
EP - 165
AB - 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.
LA - eng
KW - parabolic equations of fractional order; regular solutions; Schauder-type estimates; quasi-stationary Stefan problem with the Gibbs-Thomson correction; Besov-Slobodetskiĭ class
UR - http://eudml.org/doc/284366
ER -