A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the t...

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Detalles Bibliográficos
Autores: Calvez, Vincent, Meunier, Nicolas
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:67743
Acceso en línea:https://ddd.uab.cat/record/67743
Access Level:acceso abierto
Palabra clave:Límits, Teoremes (Teoria de probabilitats)
Equacions
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spelling A one-dimensional Keller-Segel equation with a drift issued from the boundaryCalvez, VincentMeunier, NicolasLímits, Teoremes (Teoria de probabilitats)EquacionsWe investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).Centre de Recerca MatemàticaCentre de Recerca Matemàtica 22010-01-0120102010-01-01Articlehttp://purl.org/coar/resource_type/c_6501AOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/67743reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/2.5/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:677432026-06-06T12:50:31Z
dc.title.none.fl_str_mv A one-dimensional Keller-Segel equation with a drift issued from the boundary
title A one-dimensional Keller-Segel equation with a drift issued from the boundary
spellingShingle A one-dimensional Keller-Segel equation with a drift issued from the boundary
Calvez, Vincent
Límits, Teoremes (Teoria de probabilitats)
Equacions
title_short A one-dimensional Keller-Segel equation with a drift issued from the boundary
title_full A one-dimensional Keller-Segel equation with a drift issued from the boundary
title_fullStr A one-dimensional Keller-Segel equation with a drift issued from the boundary
title_full_unstemmed A one-dimensional Keller-Segel equation with a drift issued from the boundary
title_sort A one-dimensional Keller-Segel equation with a drift issued from the boundary
dc.creator.none.fl_str_mv Calvez, Vincent
Meunier, Nicolas
author Calvez, Vincent
author_facet Calvez, Vincent
Meunier, Nicolas
author_role author
author2 Meunier, Nicolas
author2_role author
dc.contributor.none.fl_str_mv Centre de Recerca Matemàtica
dc.subject.none.fl_str_mv Límits, Teoremes (Teoria de probabilitats)
Equacions
topic Límits, Teoremes (Teoria de probabilitats)
Equacions
description We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).
publishDate 2010
dc.date.none.fl_str_mv 2
2010-01-01
2010
2010-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/67743
url https://ddd.uab.cat/record/67743
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
https://creativecommons.org/licenses/by-nc-nd/2.5/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/2.5/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Centre de Recerca Matemàtica
publisher.none.fl_str_mv Centre de Recerca Matemàtica
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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repository.mail.fl_str_mv
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