Abstract and Applied Analysis

Bifurcation of the equivariant minimal interfaces in a hydromechanics problem

A. Y. Borisovich and W. Marzantowicz

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 7 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049726053

Digital Object Identifier
doi:10.1155/S1085337596000152

Mathematical Reviews number (MathSciNet)
MR1485578

Zentralblatt MATH identifier
0942.58025

Subjects
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

Keywords
Equivariant Plateau problem fluid interface bifurcation

Citation

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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References

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