Stability of the blow-up time and the blow-up set under perturbations

Autores
Arrieta, José M.; Ferreira, Raúl; de Pablo, Arturo; Rossi, Julio Daniel
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among them we consider changing the spacial domain in which the heat equation with a power source takes place. We consider rather general perturbations of the domain and show the continuity of the blowup time. Moreover, we deal with perturbations on the initial condition and on parameters in the equation. Finally, we also present some continuity results for the blow-up set.
Fil: Arrieta, José M.. Universidad Complutense de Madrid; España
Fil: Ferreira, Raúl. Universidad Complutense de Madrid; España
Fil: de Pablo, Arturo. Universidad Carlos III de Madrid; España
Fil: Rossi, Julio Daniel. Universidad Autónoma de Madrid; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Stability
Blow-up
Perturbations
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:11336/16472
Acceder
id CONICETDig_d2241120f6078cbd29bd75a870b6258d
oai_identifier_str oai:ri.conicet.gov.ar:11336/16472
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Stability of the blow-up time and the blow-up set under perturbationsArrieta, José M.Ferreira, Raúlde Pablo, ArturoRossi, Julio DanielStabilityBlow-upPerturbationshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among them we consider changing the spacial domain in which the heat equation with a power source takes place. We consider rather general perturbations of the domain and show the continuity of the blowup time. Moreover, we deal with perturbations on the initial condition and on parameters in the equation. Finally, we also present some continuity results for the blow-up set.Fil: Arrieta, José M.. Universidad Complutense de Madrid; EspañaFil: Ferreira, Raúl. Universidad Complutense de Madrid; EspañaFil: de Pablo, Arturo. Universidad Carlos III de Madrid; EspañaFil: Rossi, Julio Daniel. Universidad Autónoma de Madrid; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmer Inst Mathematical Sciences2010-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/16472Arrieta, José M.; Ferreira, Raúl; de Pablo, Arturo; Rossi, Julio Daniel; Stability of the blow-up time and the blow-up set under perturbations; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 26; 1; 1-2010; 43-611078-09471553-5231enginfo:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2010.26.43info:eu-repo/semantics/altIdentifier/url/http://www.aimsciences.org/journals/displayArticles.jsp?paperID=4548info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:41:08Zoai:ri.conicet.gov.ar:11336/16472instacron: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:34982025-09-29 09:41:09.09CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Stability of the blow-up time and the blow-up set under perturbations
title Stability of the blow-up time and the blow-up set under perturbations
spellingShingle Stability of the blow-up time and the blow-up set under perturbations
Arrieta, José M.
Stability
Blow-up
Perturbations
title_short Stability of the blow-up time and the blow-up set under perturbations
title_full Stability of the blow-up time and the blow-up set under perturbations
title_fullStr Stability of the blow-up time and the blow-up set under perturbations
title_full_unstemmed Stability of the blow-up time and the blow-up set under perturbations
title_sort Stability of the blow-up time and the blow-up set under perturbations
dc.creator.none.fl_str_mv Arrieta, José M.
Ferreira, Raúl
de Pablo, Arturo
Rossi, Julio Daniel
author Arrieta, José M.
author_facet Arrieta, José M.
Ferreira, Raúl
de Pablo, Arturo
Rossi, Julio Daniel
author_role author
author2 Ferreira, Raúl
de Pablo, Arturo
Rossi, Julio Daniel
author2_role author
author
author
dc.subject.none.fl_str_mv Stability
Blow-up
Perturbations
topic Stability
Blow-up
Perturbations
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among them we consider changing the spacial domain in which the heat equation with a power source takes place. We consider rather general perturbations of the domain and show the continuity of the blowup time. Moreover, we deal with perturbations on the initial condition and on parameters in the equation. Finally, we also present some continuity results for the blow-up set.
Fil: Arrieta, José M.. Universidad Complutense de Madrid; España
Fil: Ferreira, Raúl. Universidad Complutense de Madrid; España
Fil: de Pablo, Arturo. Universidad Carlos III de Madrid; España
Fil: Rossi, Julio Daniel. Universidad Autónoma de Madrid; España. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among them we consider changing the spacial domain in which the heat equation with a power source takes place. We consider rather general perturbations of the domain and show the continuity of the blowup time. Moreover, we deal with perturbations on the initial condition and on parameters in the equation. Finally, we also present some continuity results for the blow-up set.
publishDate 2010
dc.date.none.fl_str_mv 2010-01
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/11336/16472
Arrieta, José M.; Ferreira, Raúl; de Pablo, Arturo; Rossi, Julio Daniel; Stability of the blow-up time and the blow-up set under perturbations; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 26; 1; 1-2010; 43-61
1078-0947
1553-5231
url http://hdl.handle.net/11336/16472
identifier_str_mv Arrieta, José M.; Ferreira, Raúl; de Pablo, Arturo; Rossi, Julio Daniel; Stability of the blow-up time and the blow-up set under perturbations; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 26; 1; 1-2010; 43-61
1078-0947
1553-5231
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2010.26.43
info:eu-repo/semantics/altIdentifier/url/http://www.aimsciences.org/journals/displayArticles.jsp?paperID=4548
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 Amer Inst Mathematical Sciences
publisher.none.fl_str_mv Amer Inst Mathematical Sciences
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_ 1844613300438958080
score 13.070432

Publicaciones similares