Proceedings of the American Mathematical Society

Author(s): Björn Gustafsson; Dmitri Prokhorov; Alexander Vasil'ev
Journal: Proc. Amer. Math. Soc. 132 (2004), 2661-2669.
MSC (2000): Primary 30C45, 76D27, 76S05; Secondary 35Q35, 30C35
Posted: April 8, 2004
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30C45, 76D27, 76S05, 35Q35, 30C35

Björn Gustafsson
Affiliation: Department of Mathematics, Royal Institute of Technology, Stockholm 100 44, Sweden
Email: gbjorn@math.kth.se

Dmitri Prokhorov
Affiliation: Department of Mathematics and Mechanics, Saratov State University, Saratov 410012, Russia
Email: ProkhorovDV@info.sgu.ru

Alexander Vasil'ev
Affiliation: Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile
Email: alexander.vasiliev@mat.utfsm.cl

DOI: 10.1090/S0002-9939-04-07419-2
PII: S 0002-9939(04)07419-2
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
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society

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