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1998 Crystalline version of the Stefan problem with Gibbs-Thompson law and kinetic undercooling
Piotr Rybka
Adv. Differential Equations 3(5): 687-713 (1998).

Abstract

The author studies the modified Stefan problem in the plane with surface tension and kinetic undercooling when the interfacial curve is a polygon. Existence of local-in-time solutions is shown. Geometric properties of the flow are studied if the Wulff shape is a regular $N$-sided polygon. The author shows that an initial interface being a scaled Wulff shape with sufficiently small perimeter shrinks to a point. Moreover, at each time the interface remains a scaled Wulff shape.

Citation

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Piotr Rybka. "Crystalline version of the Stefan problem with Gibbs-Thompson law and kinetic undercooling." Adv. Differential Equations 3 (5) 687 - 713, 1998.

Information

Published: 1998
First available in Project Euclid: 18 April 2013

zbMATH: 0949.35148
MathSciNet: MR1665866

Subjects:
Primary: 35R35
Secondary: 35K99, 73B30, 73B40, 80A22

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.3 • No. 5 • 1998
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