Strongly 桅-like functions of order 伪 in two-dimensional free boundary problems

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• 作者：Denisa Fericean ^{denisa.fericean@ubbcluj.ro}
• 关键词：Conformal map ; Free boundary problem ; Hele&ndash ; Shaw flow ; Spirallike function ; Starlike function ; Strongly 桅-like function ; Surface tension
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：1 April, 2012
• 卷：218
• 期：15
• 页码：7856-7863
• 文件大小：278 K

摘要

In this paper we apply certain results in the theory of univalent functions to investigate the time evolution of the free boundary of a viscous fluid for a planar flow problem in the Hele-Shaw cell model under injection. To this end, we prove that the property of strongly 桅-likeness of order 伪 鈭?#xA0;(0, 1] is preserved in time for both inner and outer problems, under the assumption of nonzero small surface tension.