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Hele-Shaw flow on hyperbolic surfaces
KTH, Superseded Departments, Mathematics.
2002 (English)In: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, Vol. 81, no 3, 187-222 p.Article in journal (Refereed) Published
Abstract [en]

Consider a complete simply connected hyperbolic surface. The classical Hadamard theorem asserts that at each point of the surface, the exponential mapping from the tangent plane to the surface defines a global diffeomorphism. This can be interpreted as a statement relating the metric flow on the tangent plane with that of the surface. We find an analogue of Hadamard's theorem with metric flow replaced by Hele-Shaw flow, which models the injection of (two-dimensional) fluid into the surface. The Hele-Shaw flow domains are characterized implicitly by a mean value property on harmonic functions.

Place, publisher, year, edition, pages
2002. Vol. 81, no 3, 187-222 p.
Keyword [en]
Hele-Shaw flow, mean value identifies, hyperbolic surface, exponential mapping, moving boundary-problem, variational-inequalities, potential-theory, bergman spaces
URN: urn:nbn:se:kth:diva-21490ISI: 000175191900001OAI: diva2:340188
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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Hedenmalm, HåkanShimorin, Serguei
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