# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## On the Stefan problem with a small parameter

### Tom 81 / 2008

Banach Center Publications 81 (2008), 43-63 MSC: Primary 35R35; Secondary 35B25, 35K60, 80A22. DOI: 10.4064/bc81-0-3

#### Streszczenie

We consider the multidimensional two-phase Stefan problem with a small parameter $\kappa$ in the Stefan condition, due to which the problem becomes singularly perturbed. We prove unique solvability and a coercive uniform (with respect to $\kappa$) estimate of the solution of the Stefan problem for $t\le T_0$, $T_0$ independent of $\kappa$, and the existence and estimate of the solution of the Florin problem (Stefan problem with $\kappa=0$) in Hölder spaces.

#### Autorzy

• Galina I. BizhanovaInstitute of Mathematics
Pushkin St. 125
Almaty, 050010, Kazakhstan
e-mail

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