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

Paula Curt and Denisa Fericean

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

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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https://doi.org/10.1155/2011/948236

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:948236

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