Non-Trivial Self-Similar Extinction Solutions for a 3D Hele–Shaw Suction Problem
E. Vondenhoff
TU Eindhoven, NetherlandsGeorg Prokert
TU Eindhoven, Netherlands

Abstract
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.
Cite this article
E. Vondenhoff, Georg Prokert, Non-Trivial Self-Similar Extinction Solutions for a 3D Hele–Shaw Suction Problem. Z. Anal. Anwend. 28 (2009), no. 2, pp. 183–188
DOI 10.4171/ZAA/1379