A Special Class of Univalent Functions in Hele-Shaw Flow Problems

Paula Curt and Denisa Fericean

Abstract and Applied Analysis, 2011, vol. 2011, 1-10

Abstract:

We study the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shaw cells under injection. Applying methods from the theory of univalent functions, we prove the invariance in time of Φ -likeness property (a geometric property which includes starlikeness and spiral-likeness) for two basic cases: the inner problem and the outer problem. We study both zero and nonzero surface tension models. Certain particular cases are also presented.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:948236

DOI: 10.1155/2011/948236

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