Bifurcation of the equivariant minimal interfaces in a hydromechanics problem
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...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | Abstract and Applied Analysis |
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| Online Access: | http://dx.doi.org/10.1155/S1085337596000152 |
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| _version_ | 1832565422842445824 |
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| author | A. Y. Borisovich W. Marzantowicz |
| author_facet | A. Y. Borisovich W. Marzantowicz |
| author_sort | A. Y. Borisovich |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-14082366076e4018a629d5e3ef14cf51 |
| institution | Kabale University |
| issn | 1085-3375 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-14082366076e4018a629d5e3ef14cf512025-02-03T01:07:48ZengWileyAbstract and Applied Analysis1085-33751996-01-011329130410.1155/S1085337596000152Bifurcation of the equivariant minimal interfaces in a hydromechanics problemA. Y. Borisovich0W. Marzantowicz1Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, Gdańsk 80-952, PolandInstitute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, Gdańsk 80-952, PolandIn 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.http://dx.doi.org/10.1155/S1085337596000152Equivariant Plateau problemfluid interfacebifurcation. |
| spellingShingle | A. Y. Borisovich W. Marzantowicz Bifurcation of the equivariant minimal interfaces in a hydromechanics problem Abstract and Applied Analysis Equivariant Plateau problem fluid interface bifurcation. |
| title | Bifurcation of the equivariant minimal interfaces in a hydromechanics problem |
| title_full | Bifurcation of the equivariant minimal interfaces in a hydromechanics problem |
| title_fullStr | Bifurcation of the equivariant minimal interfaces in a hydromechanics problem |
| title_full_unstemmed | Bifurcation of the equivariant minimal interfaces in a hydromechanics problem |
| title_short | Bifurcation of the equivariant minimal interfaces in a hydromechanics problem |
| title_sort | bifurcation of the equivariant minimal interfaces in a hydromechanics problem |
| topic | Equivariant Plateau problem fluid interface bifurcation. |
| url | http://dx.doi.org/10.1155/S1085337596000152 |
| work_keys_str_mv | AT ayborisovich bifurcationoftheequivariantminimalinterfacesinahydromechanicsproblem AT wmarzantowicz bifurcationoftheequivariantminimalinterfacesinahydromechanicsproblem |