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Infinite lifetime for the starlike dynamics in Hele-Shaw cells

Authors: Björn Gustafsson, Dmitri Prokhorov and Alexander Vasil'ev
Journal: Proc. Amer. Math. Soc. 132 (2004), 2661-2669
MSC (2000): Primary 30C45, 76D27, 76S05; Secondary 35Q35, 30C35
Published electronically: April 8, 2004
MathSciNet review: 2054792
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Abstract | References | Similar Articles | Additional Information

Abstract: One of the ``folklore" questions in the theory of free boundary problems is the lifetime of the starlike dynamics in a Hele-Shaw cell. We prove precisely that, starting with a starlike analytic phase domain $\Omega_0$, the Hele-Shaw chain of subordinating domains $\Omega(t)$, $\Omega_0=\Omega(0)$, exists for an infinite time under injection at the point of starlikeness.

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Additional Information

Björn Gustafsson
Affiliation: Department of Mathematics, Royal Institute of Technology, Stockholm 100 44, Sweden

Dmitri Prokhorov
Affiliation: Department of Mathematics and Mechanics, Saratov State University, Saratov 410012, Russia

Alexander Vasil'ev
Affiliation: Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile

Keywords: Free boundary problem, Hele-Shaw flow, univalent function, starlike function, L\"owner-Kufarev equation
Received by editor(s): January 3, 2003
Received by editor(s) in revised form: June 10, 2003
Published electronically: April 8, 2004
Additional Notes: The first author was partially supported by the Swedish Research Council, the Göran Gustafsson Foundation, and Fondecyt (Chile) # 7030011. The second author was supported by Fondecyt (Chile) # 7010093, and the third author was partially supported by Projects Fondecyt (Chile) # 1030373, 1020067, and UTFSM 12.03.23.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society