Abstract
We study the modified Stefan problem in the plane for polygonal interfacial curves. Uniqueness of local in time solutions is shown while existence of local in time solutions has been proved in an earlier work of the author [P. Rybka, Advances in Differential Equations, 3 (1998), pp. 687--713]. Geometric properties of the flow are studied if the Wulff shape is a regular N-sided polygon and the initial interface has sufficiently small perimeter. Namely, if the isoperimetric quotient of the initial interface does not differ much from the isoperimetric quotient of the Wulff shape, then the interface shrinks to a point in finite time and the isoperimetric quotient decreases.
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