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Classification of degree three polynomial solutions to the Polubarinova–Galin equation

Published online by Cambridge University Press:  04 May 2015

YU-LIN LIN
YU-LIN LIN*
Affiliation:
Royal Institute of Technology, Stockholm, Sweden email: [email protected]
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Abstract

The Polubarinova–Galin equation describes a parametric conformal map for the zero-surface-tension Hele-Shaw flow driven by injection or suction. In this paper, we classify degree three polynomial solutions to the Polubarinova–Galin equation into three categories: global solutions, solutions which can be continued after blow-up and solutions which cannot be continued after blow-up. The coefficient region of the initial functions in each category is obtained.

Keywords

Hele-Shawclassification of solutionsPolubarinova-Galin equation
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 6 , December 2015 , pp. 849 - 861
Copyright
Copyright © Cambridge University Press 2015 

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