Advances in Differential Equations

Crystalline version of the Stefan problem with Gibbs-Thompson law and kinetic undercooling

Piotr Rybka

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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.

Article information

Adv. Differential Equations, Volume 3, Number 5 (1998), 687-713.

First available in Project Euclid: 18 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 35K99: None of the above, but in this section 73B30 73B40 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


Rybka, Piotr. Crystalline version of the Stefan problem with Gibbs-Thompson law and kinetic undercooling. Adv. Differential Equations 3 (1998), no. 5, 687--713.

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