Abstract and Applied Analysis
Volume 2011 (2011), Article ID 948236, 10 pages
doi:10.1155/2011/948236
Research Article

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

1Faculty of Economics and Business Administration, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania
2Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

Received 7 December 2010; Accepted 23 February 2011

Academic Editor: Yoshikazu Giga

Copyright © 2011 Paula Curt and Denisa Fericean. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.