Complex variable methods in Hele–Shaw moving boundary problems
Complex variable methods in Hele–Shaw moving boundary problems
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DOI：
10.1017/s0956792500000802
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发表时间：
1992-09
影响因子：
1.9
通讯作者：
S. Howison
中科院分区：
文献类型：
--
作者：
S. Howison
We discuss the one-phase Hele–Shaw problem in two space dimensions. We review exact solutions in the zero-surface-tension case, giving a unified account of the Schwarz function and conformal mapping approaches. We discuss the extension of the former method to the cases in which surface tension or ‘kinetic undercooling’ terms apply on the moving boundary, and we give some conjectures on the resulting singularity structure. Finally, we give a new interpretation of the linear stability analysis of the zero-surface-tension problem, and we suggest a possible regularization of ill-posed problems by the imposition of a unilateral constraint on the moving boundary.
