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Global in time solution to the Hele-Shaw problem with a change of topology

Published online by Cambridge University Press:  25 September 2002

ANVARBEK M. MEIRMANOV  and
BORIS ZALTZMAN
ANVARBEK M. MEIRMANOV
Affiliation:
Universidade da Beira Interior, Covilhã 6200, Portugal
BORIS ZALTZMAN
Affiliation:
DSEEP, Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede-Boqer Campus 84990, Israel
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Abstract

The existence of classical solutions with a free boundary changing its topology in time is proved for the multi-dimensional Hele-Shaw problem. We prove that, if some symmetry and monotonicity conditions on the problem data hold, then a cusp, arising at the contact between two free boundary components, disappears instantly and the free boundary becomes smooth and singly-connected.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 4 , August 2002 , pp. 431 - 447
Copyright
2002 Cambridge University Press

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