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Zeitschrift für Analysis und ihre Anwendungen


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Volume 28, Issue 2, 2009, pp. 183–188
DOI: 10.4171/ZAA/1379

Published online: 2009-06-30

Non-Trivial Self-Similar Extinction Solutions for a 3D Hele–Shaw Suction Problem

Georg Prokert[1] and E. Vondenhoff[2]

(1) TU Eindhoven, Netherlands
(2) TU Eindhoven, Netherlands

We show the existence of noncircular, self-similar solutions to the three-dimen\-sional Hele--Shaw suction problem with surface tension regularisation up to complete extinction. In an appropriate scaling, these solutions are found as bifurcation solutions to a nonlocal elliptic equation of order three. The bifurcation parameter is the ratio of the suction speed and the surface tension coefficient.

Keywords: Hele–Shaw flow, bifurcation solution

Prokert Georg, Vondenhoff E.: Non-Trivial Self-Similar Extinction Solutions for a 3D Hele–Shaw Suction Problem. Z. Anal. Anwend. 28 (2009), 183-188. doi: 10.4171/ZAA/1379