Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support
We study the transient flow of an isothermal and incompressible Bingham fluid. Similar models arise in completely different contexts as, for instance, in material science, image processing and differential geometry. For the two-dimensional flow in a bounded domain we show the extinction in a finite...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/42155 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/42155 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.928 517.956.2 Equations Bingham flows propagation of the support stabilzation finite extinction time numerical experiences Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
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Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the supportDíaz Díaz, Jesús IldefonsoGlowinski, R.Guidoboni, G.Kim, T.517.928517.956.2EquationsBingham flowspropagation of the supportstabilzationfinite extinction timenumerical experiencesEcuaciones diferenciales1202.07 Ecuaciones en DiferenciasWe study the transient flow of an isothermal and incompressible Bingham fluid. Similar models arise in completely different contexts as, for instance, in material science, image processing and differential geometry. For the two-dimensional flow in a bounded domain we show the extinction in a finite time even under suitable nonzero external forces. We also consider the special case of a three-dimensional domain given as an infinitely long cylinder of bounded cross section. We give sufficient conditions leading to a scalar formulation on the cross section. We prove the stabilization of solutions, when t goes to infinity, to the solution u(infinity) of the associated stationary problem, once we assume a suitable convergence on the right hand forcing term. We give some sufficient conditions for the extinction in a finite time of solutions of the scalar problem. We show that, at least under radially symmetric conditions, when the stationary state is not trivial, u(infinity) not equal 0, there are cases in which the stabilization to the stationary solution needs an infinite time to take place. We end the paper with some numerical experiences on the scalar formulation. In particular, some of those experiences exhibit an instantaneous change of topology of the support of the solution: when the support of the initial datum is formed by two disjoint balls, but closed enough, then, instantaneously, for any t > 0, the support of the solution u(., t) becomes a connected set. Some other numerical experiences are devoted to the study of the "profile" of the solution and its extinction time.Real Academia Ciencias Exactas Físicas Y NaturalesUniversidad Complutense de Madrid20102010-01-0120102010-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/42155reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/421552026-06-02T12:44:21Z |
| dc.title.none.fl_str_mv |
Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support |
| title |
Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support |
| spellingShingle |
Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support Díaz Díaz, Jesús Ildefonso 517.928 517.956.2 Equations Bingham flows propagation of the support stabilzation finite extinction time numerical experiences Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| title_short |
Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support |
| title_full |
Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support |
| title_fullStr |
Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support |
| title_full_unstemmed |
Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support |
| title_sort |
Qualitative properties and approximation of solutions of Bingham flows: on the stabilization for large time and the geometry of the support |
| dc.creator.none.fl_str_mv |
Díaz Díaz, Jesús Ildefonso Glowinski, R. Guidoboni, G. Kim, T. |
| author |
Díaz Díaz, Jesús Ildefonso |
| author_facet |
Díaz Díaz, Jesús Ildefonso Glowinski, R. Guidoboni, G. Kim, T. |
| author_role |
author |
| author2 |
Glowinski, R. Guidoboni, G. Kim, T. |
| author2_role |
author author author |
| dc.contributor.none.fl_str_mv |
Universidad Complutense de Madrid |
| dc.subject.none.fl_str_mv |
517.928 517.956.2 Equations Bingham flows propagation of the support stabilzation finite extinction time numerical experiences Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| topic |
517.928 517.956.2 Equations Bingham flows propagation of the support stabilzation finite extinction time numerical experiences Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| description |
We study the transient flow of an isothermal and incompressible Bingham fluid. Similar models arise in completely different contexts as, for instance, in material science, image processing and differential geometry. For the two-dimensional flow in a bounded domain we show the extinction in a finite time even under suitable nonzero external forces. We also consider the special case of a three-dimensional domain given as an infinitely long cylinder of bounded cross section. We give sufficient conditions leading to a scalar formulation on the cross section. We prove the stabilization of solutions, when t goes to infinity, to the solution u(infinity) of the associated stationary problem, once we assume a suitable convergence on the right hand forcing term. We give some sufficient conditions for the extinction in a finite time of solutions of the scalar problem. We show that, at least under radially symmetric conditions, when the stationary state is not trivial, u(infinity) not equal 0, there are cases in which the stabilization to the stationary solution needs an infinite time to take place. We end the paper with some numerical experiences on the scalar formulation. In particular, some of those experiences exhibit an instantaneous change of topology of the support of the solution: when the support of the initial datum is formed by two disjoint balls, but closed enough, then, instantaneously, for any t > 0, the support of the solution u(., t) becomes a connected set. Some other numerical experiences are devoted to the study of the "profile" of the solution and its extinction time. |
| publishDate |
2010 |
| dc.date.none.fl_str_mv |
2010 2010-01-01 2010 2010-01-01 |
| dc.type.none.fl_str_mv |
journal article http://purl.org/coar/resource_type/c_6501 |
| dc.type.openaire.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/20.500.14352/42155 |
| url |
https://hdl.handle.net/20.500.14352/42155 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 |
| dc.rights.openaire.fl_str_mv |
info:eu-repo/semantics/openAccess |
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open access http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
Real Academia Ciencias Exactas Físicas Y Naturales |
| publisher.none.fl_str_mv |
Real Academia Ciencias Exactas Físicas Y Naturales |
| dc.source.none.fl_str_mv |
reponame:Docta Complutense instname:Universidad Complutense de Madrid (UCM) |
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Universidad Complutense de Madrid (UCM) |
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Docta Complutense |
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Docta Complutense |
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15,300724 |