Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up

Autores
Brändle, Cristina; Quirós, Fernando; Rossi, Julio Daniel
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the possibility of defining a nontrivial continuation after the blow-up time for a system of two heat equations with a nonlinear coupling at the boundary. It turns out that any possible continuation that verify a maximum principle is identically infinity after the blow-up time, that is, both components blow up completely. We also analyze the propagation of the singularity to the whole space, the avalanche, when blow-up is non-simultaneous.
Fil: Brändle, Cristina. Universidad Carlos III de Madrid. Departamento de Matemáticas; Argentina
Fil: Quirós, Fernando. Universidad Autónoma de Madrid; España
Fil: Rossi, Julio Daniel. Universidad Autónoma de Madrid; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Complete blow-up
Parabolic system
Nonlinear boundary conditions
Avalanche
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/16376
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/16376
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-upBrändle, CristinaQuirós, FernandoRossi, Julio DanielComplete blow-upParabolic systemNonlinear boundary conditionsAvalanchehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the possibility of defining a nontrivial continuation after the blow-up time for a system of two heat equations with a nonlinear coupling at the boundary. It turns out that any possible continuation that verify a maximum principle is identically infinity after the blow-up time, that is, both components blow up completely. We also analyze the propagation of the singularity to the whole space, the avalanche, when blow-up is non-simultaneous.Fil: Brändle, Cristina. Universidad Carlos III de Madrid. Departamento de Matemáticas; ArgentinaFil: Quirós, Fernando. Universidad Autónoma de Madrid; EspañaFil: Rossi, Julio Daniel. Universidad Autónoma de Madrid; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaDe Gruyter2010-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/16376Brändle, Cristina; Quirós, Fernando; Rossi, Julio Daniel; Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up; De Gruyter; Advanced Nonlinear Studies; 10; 3; 8-2010; 659-6791536-13652169-0375enginfo:eu-repo/semantics/altIdentifier/doi/10.1515/ans-2010-0308info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/ans.2010.10.issue-3/ans-2010-0308/ans-2010-0308.xmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:12:28Zoai:ri.conicet.gov.ar:11336/16376instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:12:28.414CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
title Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
spellingShingle Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
Brändle, Cristina
Complete blow-up
Parabolic system
Nonlinear boundary conditions
Avalanche
title_short Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
title_full Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
title_fullStr Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
title_full_unstemmed Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
title_sort Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up
dc.creator.none.fl_str_mv Brändle, Cristina
Quirós, Fernando
Rossi, Julio Daniel
author Brändle, Cristina
author_facet Brändle, Cristina
Quirós, Fernando
Rossi, Julio Daniel
author_role author
author2 Quirós, Fernando
Rossi, Julio Daniel
author2_role author
author
dc.subject.none.fl_str_mv Complete blow-up
Parabolic system
Nonlinear boundary conditions
Avalanche
topic Complete blow-up
Parabolic system
Nonlinear boundary conditions
Avalanche
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the possibility of defining a nontrivial continuation after the blow-up time for a system of two heat equations with a nonlinear coupling at the boundary. It turns out that any possible continuation that verify a maximum principle is identically infinity after the blow-up time, that is, both components blow up completely. We also analyze the propagation of the singularity to the whole space, the avalanche, when blow-up is non-simultaneous.
Fil: Brändle, Cristina. Universidad Carlos III de Madrid. Departamento de Matemáticas; Argentina
Fil: Quirós, Fernando. Universidad Autónoma de Madrid; España
Fil: Rossi, Julio Daniel. Universidad Autónoma de Madrid; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study the possibility of defining a nontrivial continuation after the blow-up time for a system of two heat equations with a nonlinear coupling at the boundary. It turns out that any possible continuation that verify a maximum principle is identically infinity after the blow-up time, that is, both components blow up completely. We also analyze the propagation of the singularity to the whole space, the avalanche, when blow-up is non-simultaneous.
publishDate 2010
dc.date.none.fl_str_mv 2010-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/16376
Brändle, Cristina; Quirós, Fernando; Rossi, Julio Daniel; Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up; De Gruyter; Advanced Nonlinear Studies; 10; 3; 8-2010; 659-679
1536-1365
2169-0375
url http://hdl.handle.net/11336/16376
identifier_str_mv Brändle, Cristina; Quirós, Fernando; Rossi, Julio Daniel; Complete Blow-up and Avalanche Formation for a Parabolic System with Non-Simultaneous Blow-up; De Gruyter; Advanced Nonlinear Studies; 10; 3; 8-2010; 659-679
1536-1365
2169-0375
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1515/ans-2010-0308
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/ans.2010.10.issue-3/ans-2010-0308/ans-2010-0308.xml
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1846083273123430400
score 13.22299

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