Non-trivial self-similar extinction solutions for a 3D Hele-Shaw suction problem

G. Prokert, E. Vondenhoff

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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.
Original languageEnglish
Pages (from-to)183-188
JournalZeitschrift für Analysis und Ihre Anwendungen
Volume28
Issue number2
DOIs
Publication statusPublished - 2009

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