Infinite lifetime for the starlike dynamics in Hele-Shaw cells
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- by Björn Gustafsson, Dmitri Prokhorov and Alexander Vasil’ev PDF
- Proc. Amer. Math. Soc. 132 (2004), 2661-2669 Request permission
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.References
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Additional Information
- 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
- MR Author ID: 225056
- Email: alexander.vasiliev@mat.utfsm.cl
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2661-2669
- MSC (2000): Primary 30C45, 76D27, 76S05; Secondary 35Q35, 30C35
- DOI: https://doi.org/10.1090/S0002-9939-04-07419-2
- MathSciNet review: 2054792