Solutions for the Two-Phase Stefan Problem with the Gibbs—Thomson Law for the Melting Temperature
Solutions for the Two-Phase Stefan Problem with the Gibbs—Thomson Law for the Melting Temperature
复制标题
两相 Stefan 问题的吉布斯熔化温度汤姆逊定律的解
DOI：
10.1007/978-3-642-59938-5_12
复制
发表时间：
1990
影响因子：
1.9
通讯作者：
S. Luckhaus
中科院分区：
文献类型：
--
作者：
S. Luckhaus
考虑了热流 Stefan 方程与熔化温度与相界面平均曲率相关的 Gibbs-Thomson 定律的耦合。构建时间上全局的解决方案以满足自然先验估计。数学上的主要困难是分别证明温度和相位指示函数在时间上的一定规律性。容量类型估计用于给出分数时间导数的 Lx 界限。
The coupling of the Stefan equation for the heat flow with the Gibbs-Thomson law relating the melting temperature to the mean curvature of the phase interface is considered. Solutions, global in time, are constructed which satisfy the natural a priori estimates. Mathematically the main difficulty is to prove a certain regularity in time for the temperature and the indicator function of the phase separately. A capacity type estimate is used to give an Lx bound for fractional time derivatives.