Abstract and Applied Analysis

Bifurcation of the equivariant minimal interfaces in a hydromechanics problem

A. Y. Borisovich and W. Marzantowicz

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In this work we study a deformation of the minimal interface of two fluids in a vertical tube under the presence of gravitation. We show that a symmetry of the base of tube let us to apply a method developed earlier by the first author and based on the Crandall-Rabinowitz bifurcation theorem. Using the natural symmetry of the corresponding variational problem defined by a symmetry of region and restricting the functional to spaces of invariant functions we show the existence of bifurcation, and describe its local picture, for interfaces parametrized by the square and disc.

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Abstr. Appl. Anal., Volume 1, Number 3 (1996), 291-304.

First available in Project Euclid: 7 April 2003

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Zentralblatt MATH identifier

Primary: 58E12: Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C10: $G$-structures

Equivariant Plateau problem fluid interface bifurcation


Borisovich, A. Y.; Marzantowicz, W. Bifurcation of the equivariant minimal interfaces in a hydromechanics problem. Abstr. Appl. Anal. 1 (1996), no. 3, 291--304. doi:10.1155/S1085337596000152. https://projecteuclid.org/euclid.aaa/1049726053

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