Volume 9, Issue 2
The Limit of the Stefan Problem with Surface Tension and Kinetic Undercooling on the Free Boundary

J. Part. Diff. Eq., 9 (1996), pp. 153-168.

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• Abstract

In this paper we consider the Stefan problem with surface tension and kinetic undercooling effects, that is with the temperature u satisfying the condition u = -σK - εV_n on the interface Γ_t, σ, ε = const. ≥ 0 where K and V_n are the mean curvature and the normal velocity of Γ_t, respectively. In any of the following situations: (1) σ > 0 fixed, ε > 0, (2) σ = ε → 0; (3) σ → 0, ε = 0, we shall prove the convergence of the corresponding local (in time) classical solution of the Stefan problem.

• History

Published online: 1996-09

• Keywords