JournalszaaVol. 28, No. 2pp. 183–188

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

  • E. Vondenhoff

    TU Eindhoven, Netherlands
  • Georg Prokert

    TU Eindhoven, Netherlands
Non-Trivial Self-Similar Extinction Solutions for a 3D Hele–Shaw Suction Problem cover
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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