Ukrainian Mathematical Bulletin

Volume 1, Issue 1, 2004 pp. 53-65.

The Stefan Problem with Surface Tension

Authors: M.A.Borodin
Author institution: Department of Mathematical Physics, Donetsk National University, Ukraine

Summary: In this paper we study a free-boundary problem for a parabolic equation. This problem differs from the Stefan problem by one of the boundary conditions containing the curvature of an unknown boundary. We prove the existence of a global classical solution of the problem under consideration in the case of two space variables and give a description of the free boundary in terms of smooth functions.

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