A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis
We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori e...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/152743 |
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| author | R. Fares G. P. Panasenko R. Stavre |
| author_facet | R. Fares G. P. Panasenko R. Stavre |
| author_sort | R. Fares |
| collection | DOAJ |
| description | We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions. |
| format | Article |
| id | doaj-art-05b9baf5d7bb45fbacc60d5b965a3a6e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-05b9baf5d7bb45fbacc60d5b965a3a6e2025-02-03T05:59:34ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/152743152743A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic AnalysisR. Fares0G. P. Panasenko1R. Stavre2Institut Camille Jordan UMR, CNRS 5208, PRES University of Lyon/University of Saint-Etienne, 23 Rue Paul Michelon, 42023 Saint-Etienne, FranceInstitut Camille Jordan UMR, CNRS 5208, PRES University of Lyon/University of Saint-Etienne, 23 Rue Paul Michelon, 42023 Saint-Etienne, FranceInstitute of Mathematics “Simion Stoilow”, Romanian Academy, P.O. Box 1-764, 014 700 Bucharest, RomaniaWe study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.http://dx.doi.org/10.1155/2012/152743 |
| spellingShingle | R. Fares G. P. Panasenko R. Stavre A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis Abstract and Applied Analysis |
| title | A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis |
| title_full | A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis |
| title_fullStr | A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis |
| title_full_unstemmed | A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis |
| title_short | A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis |
| title_sort | viscous fluid flow through a thin channel with mixed rigid elastic boundary variational and asymptotic analysis |
| url | http://dx.doi.org/10.1155/2012/152743 |
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