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

Youshan Tao

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

Published online: 1996-09

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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.
  • Keywords

Limit Stefan problem lower order terms model problem Fréchet derivative

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@Article{JPDE-9-153, author = {}, title = {The Limit of the Stefan Problem with Surface Tension and Kinetic Undercooling on the Free Boundary}, journal = {Journal of Partial Differential Equations}, year = {1996}, volume = {9}, number = {2}, pages = {153--168}, 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5617.html} }
TY - JOUR T1 - The Limit of the Stefan Problem with Surface Tension and Kinetic Undercooling on the Free Boundary 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.
Youshan Tao . (2019). The Limit of the Stefan Problem with Surface Tension and Kinetic Undercooling on the Free Boundary. Journal of Partial Differential Equations. 9 (2). 153-168. doi:
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