We consider the multidimensional two-phase Stefan problem with a small parameter κ in the Stefan condition, due to which the problem becomes singularly perturbed. We prove unique solvability and a coercive uniform (with respect to κ) estimate of the solution of the Stefan problem for t ≤ T₀, T₀ independent of κ, and the existence and estimate of the solution of the Florin problem (Stefan problem with κ = 0) in Hölder spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-3,
author = {Galina I. Bizhanova},
title = {On the Stefan problem with a small parameter},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {43-63},
zbl = {1151.35109},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-3}
}
Galina I. Bizhanova. On the Stefan problem with a small parameter. Banach Center Publications, Tome 83 (2008) pp. 43-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-3/