TY - JOUR
T1 - The Limit of the Stefan Problem with Surface Tension and Kinetic Undercooling on the Free Boundary
AU - Youshan Tao 
JO - Journal of Partial Differential Equations
VL - 2
SP - 153
EP - 168
PY - 1996
DA - 1996/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5617.html
KW - Limit
KW - Stefan problem
KW - lower order terms
KW - model problem
KW - Fréchet derivative
AB -  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.