Advances in Differential Equations
- Adv. Differential Equations
- Volume 3, Number 5 (1998), 687-713.
Crystalline version of the Stefan problem with Gibbs-Thompson law and kinetic undercooling
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.
Adv. Differential Equations, Volume 3, Number 5 (1998), 687-713.
First available in Project Euclid: 18 April 2013
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Rybka, Piotr. Crystalline version of the Stefan problem with Gibbs-Thompson law and kinetic undercooling. Adv. Differential Equations 3 (1998), no. 5, 687--713. https://projecteuclid.org/euclid.ade/1366292558