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

G. Prokert; E. Vondenhoff

doi:10.4171/ZAA/1379

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 language	English
Pages (from-to)	183-188
Journal	Zeitschrift für Analysis und Ihre Anwendungen
Volume	28
Issue number	2
DOIs	https://doi.org/10.4171/ZAA/1379
Publication status	Published - 2009

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title = "Non-trivial self-similar extinction solutions for a 3D Hele-Shaw suction problem",

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.",

author = "G. Prokert and E. Vondenhoff",

year = "2009",

doi = "10.4171/ZAA/1379",

language = "English",

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AB - 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.

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DO - 10.4171/ZAA/1379

M3 - Article

SN - 0232-2064

VL - 28

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JO - Zeitschrift für Analysis und Ihre Anwendungen

JF - Zeitschrift für Analysis und Ihre Anwendungen

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ER -

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

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