The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations

Multivalued semiflows generated by evolution equations without uniqueness sometimes satisfy a semigroup set inclusion rather than equality because, for example, the concatentation of solutions satisfying an energy inequality almost everywhere may not satisfy the energy inequality at the joining time...

Descripción completa

Detalles Bibliográficos
Autores: Kloeden, Peter E., Marín Rubio, Pedro, Valero Cuadra, José
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/25955
Acceso en línea:http://hdl.handle.net/11441/25955
https://doi.org/10.1007/s11228-012-0228-x
Access Level:acceso abierto
Palabra clave:Multivalued dynamical systems
Non-strict multivalued semiflows
Non-strict and strict global attractors
3D Navier–Stokes equations
Reaction–diffusion equations
id ES_9a2dce2bff7a86a85dd2fc87119f989f
oai_identifier_str oai:idus.us.es:11441/25955
network_acronym_str ES
network_name_str España
repository_id_str
spelling The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion EquationsKloeden, Peter E.Marín Rubio, PedroValero Cuadra, JoséMultivalued dynamical systemsNon-strict multivalued semiflowsNon-strict and strict global attractors3D Navier–Stokes equationsReaction–diffusion equationsMultivalued semiflows generated by evolution equations without uniqueness sometimes satisfy a semigroup set inclusion rather than equality because, for example, the concatentation of solutions satisfying an energy inequality almost everywhere may not satisfy the energy inequality at the joining time. Such multivalued semiflows are said to be non-strict and their attractors need only be negatively semi-invariant. In this paper the problem of enveloping a non-strict multivalued dynamical system in a strict one is analyzed and their attactors are compared. Two constructions are proposed. In the first, the attainability set mapping is extending successively to be strict at the dyadic numbers, which essentially means (in the case of the Navier–Stokes system) that the energy inequality is satisfied piecewise on successively finer dyadic subintervals. The other deals directly with trajectories and their concatenations, which are then used to define a strict multivalued dynamical system. The first is shown to be applicable to the three-dimensional Navier–Stokes equations and the second to a reaction–diffusion problem without unique solutions.Springer Verlag (Germany)Ecuaciones Diferenciales y Análisis Numérico2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/25955https://doi.org/10.1007/s11228-012-0228-xreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSet-Valued and Variational Analysis, 21 (3), 517-540.http://dx.doi.org/10.1007/s11228-012-0228-xinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/259552026-06-17T12:51:07Z
dc.title.none.fl_str_mv The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations
title The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations
spellingShingle The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations
Kloeden, Peter E.
Multivalued dynamical systems
Non-strict multivalued semiflows
Non-strict and strict global attractors
3D Navier–Stokes equations
Reaction–diffusion equations
title_short The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations
title_full The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations
title_fullStr The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations
title_full_unstemmed The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations
title_sort The Envelope Attractor of Non-Strict Multivalued Dynamical Systems with Application To The 3D Navier-Stokes and Reaction-Diffusion Equations
dc.creator.none.fl_str_mv Kloeden, Peter E.
Marín Rubio, Pedro
Valero Cuadra, José
author Kloeden, Peter E.
author_facet Kloeden, Peter E.
Marín Rubio, Pedro
Valero Cuadra, José
author_role author
author2 Marín Rubio, Pedro
Valero Cuadra, José
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Multivalued dynamical systems
Non-strict multivalued semiflows
Non-strict and strict global attractors
3D Navier–Stokes equations
Reaction–diffusion equations
topic Multivalued dynamical systems
Non-strict multivalued semiflows
Non-strict and strict global attractors
3D Navier–Stokes equations
Reaction–diffusion equations
description Multivalued semiflows generated by evolution equations without uniqueness sometimes satisfy a semigroup set inclusion rather than equality because, for example, the concatentation of solutions satisfying an energy inequality almost everywhere may not satisfy the energy inequality at the joining time. Such multivalued semiflows are said to be non-strict and their attractors need only be negatively semi-invariant. In this paper the problem of enveloping a non-strict multivalued dynamical system in a strict one is analyzed and their attactors are compared. Two constructions are proposed. In the first, the attainability set mapping is extending successively to be strict at the dyadic numbers, which essentially means (in the case of the Navier–Stokes system) that the energy inequality is satisfied piecewise on successively finer dyadic subintervals. The other deals directly with trajectories and their concatenations, which are then used to define a strict multivalued dynamical system. The first is shown to be applicable to the three-dimensional Navier–Stokes equations and the second to a reaction–diffusion problem without unique solutions.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/25955
https://doi.org/10.1007/s11228-012-0228-x
url http://hdl.handle.net/11441/25955
https://doi.org/10.1007/s11228-012-0228-x
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Set-Valued and Variational Analysis, 21 (3), 517-540.
http://dx.doi.org/10.1007/s11228-012-0228-x
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag (Germany)
publisher.none.fl_str_mv Springer Verlag (Germany)
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869414349936787456
score 15.301603

Similares en LA Referencia