A Special Class of Univalent Functions in Hele-Shaw Flow Problems-Reference-Cited by-同舟云学术

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

Published:2011 Issue: Volume:2011 Page:1-10
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Curt Paula¹,Fericean Denisa²

Affiliation:

1. Faculty of Economics and Business Administration, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania

2. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania

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 ofΦ-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.

Funder

POSDRU/88/1.5/S/60185-“Innovative Doctoral Studies in a Knowledge-Based Society”

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2011/948236.pdf

Reference14 articles.

1. Geometric properties of the solutions of a Hele-Shaw type equation

2. Convex dynamics in Hele-Shaw cells

3. Univalent Functions in the Dynamics of Viscous Flows

4. Univalent Functions in Two-Dimensional Free Boundary Problems

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