The ill-posed Hele-Shaw model and the Stefan problem for supercooled water
The ill-posed Hele-Shaw model and the Stefan problem for supercooled water
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不适定 Hele-Shaw 模型和过冷水的 Stefan 问题
DOI：
10.1090/s0002-9947-1984-0728709-6
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发表时间：
1984
影响因子：
1.3
通讯作者：
A. Friedman
中科院分区：
文献类型：
--
作者：
E. DiBenedetto;A. Friedman
.在不适定的情况下，当流体因通过核心C的吸收而后退时，分析了轻微分离板之间缓慢粘性流体的Hele-Shaw流动。在流体所占据的初始区域上给出了保证解存在的充分必要条件。自由边界的正则性是在某些相当一般的情况下建立的。类似的抛物型版本，模型的单相Stefan过冷水的问题，得到了类似的结果。
. The Hele-Shaw flow of a slow viscous fluid between slightly separated plates is analyzed in the ill-posed case when the fluid recedes due to absorption through a core C. Necessary and sufficient conditions are given on the initial domain occupied by the fluid to ensure the existence of a solution. Regularity of the free boundary is established in certain rather general cases. Similar results are obtained for the analogous parabolic version, which models the one-phase Stefan problem for supercooled water.