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

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  • Paula Curt
  • Denisa Fericean

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.

Suggested Citation

  • Paula Curt & Denisa Fericean, 2011. "A Special Class of Univalent Functions in Hele‐Shaw Flow Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:948236
    DOI: 10.1155/2011/948236
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    References listed on IDEAS

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    1. Dmitri Prokhorov & Alexander Vasil'ev, 2002. "Convex dynamics in Hele-Shaw cells," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 31, pages 1-12, January.
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