Singular limits for the two-phase Stefan problem

Jan Prüss; Jürgen Saal; Gieri Simonett

doi:10.3934/dcds.2013.33.5379

Article Contents

2013, Volume 33, Issue 11&12: 5379-5405. Doi: 10.3934/dcds.2013.33.5379

This issue Previous Article Global existence via a multivalued operator for an Allen-Cahn-Gurtin equation Next Article On the manifold of closed hypersurfaces in $\mathbb{R}^n$

Singular limits for the two-phase Stefan problem

1.
Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik, Theodor-Lieser-Strasse 5, D-06120 Halle
2.
Technische Universität Darmstadt, Center of Smart Interfaces, 64287 Darmstadt
3.
Department of Mathematics, Vanderbilt University, Nashville, TN 37240

Received: January 31, 2012

Published: October 2013

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Abstract

We prove strong convergence to singular limits for a linearized fully inhomogeneous Stefan problem subject to surface tension and kinetic undercooling effects. Different combinations of $\sigma \to \sigma_0$ and $\delta\to\delta_0$, where $\sigma,\sigma_0\ge 0$ and $\delta,\delta_0\ge 0$ denote surface tension and kinetic undercooling coefficients respectively, altogether lead to five different types of singular limits. Their strong convergence is based on uniform maximal regularity estimates.

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Mathematics Subject Classification: Primary: 35R35, 35B65, 80A22; Secondary: 35K20.

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References

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