Small random perturbations of a dynamical system with blow-up

Autores
Groisman, Pablo Jose; Saglietti, Santiago Juan
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study small random perturbations by additive white-noise of a spatial discretization of a reaction–diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and asymptotic distribution. For initial data in the domain of explosion we prove that the explosion time converges to the deterministic one while for initial data in the domain of attraction of the stable equilibrium we show that the system exhibits metastable behavior.
Fil: Groisman, Pablo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Saglietti, Santiago Juan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Blow-Up
Metastability
Stochastic Differential Equations
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19945
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19945
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Small random perturbations of a dynamical system with blow-upGroisman, Pablo JoseSaglietti, Santiago JuanBlow-UpMetastabilityStochastic Differential Equationshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study small random perturbations by additive white-noise of a spatial discretization of a reaction–diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and asymptotic distribution. For initial data in the domain of explosion we prove that the explosion time converges to the deterministic one while for initial data in the domain of attraction of the stable equilibrium we show that the system exhibits metastable behavior.Fil: Groisman, Pablo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Saglietti, Santiago Juan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaElsevier Inc2012-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19945Groisman, Pablo Jose; Saglietti, Santiago Juan; Small random perturbations of a dynamical system with blow-up; Elsevier Inc; Journal Of Mathematical Analysis And Applications; 385; 1; 1-2012; 150-1660022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2011.06.034info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X11005828info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1011.3414info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:28:45Zoai:ri.conicet.gov.ar:11336/19945instacron: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 10:28:46.076CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Small random perturbations of a dynamical system with blow-up
title Small random perturbations of a dynamical system with blow-up
spellingShingle Small random perturbations of a dynamical system with blow-up
Groisman, Pablo Jose
Blow-Up
Metastability
Stochastic Differential Equations
title_short Small random perturbations of a dynamical system with blow-up
title_full Small random perturbations of a dynamical system with blow-up
title_fullStr Small random perturbations of a dynamical system with blow-up
title_full_unstemmed Small random perturbations of a dynamical system with blow-up
title_sort Small random perturbations of a dynamical system with blow-up
dc.creator.none.fl_str_mv Groisman, Pablo Jose
Saglietti, Santiago Juan
author Groisman, Pablo Jose
author_facet Groisman, Pablo Jose
Saglietti, Santiago Juan
author_role author
author2 Saglietti, Santiago Juan
author2_role author
dc.subject.none.fl_str_mv Blow-Up
Metastability
Stochastic Differential Equations
topic Blow-Up
Metastability
Stochastic Differential Equations
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 small random perturbations by additive white-noise of a spatial discretization of a reaction–diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and asymptotic distribution. For initial data in the domain of explosion we prove that the explosion time converges to the deterministic one while for initial data in the domain of attraction of the stable equilibrium we show that the system exhibits metastable behavior.
Fil: Groisman, Pablo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Saglietti, Santiago Juan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We study small random perturbations by additive white-noise of a spatial discretization of a reaction–diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and asymptotic distribution. For initial data in the domain of explosion we prove that the explosion time converges to the deterministic one while for initial data in the domain of attraction of the stable equilibrium we show that the system exhibits metastable behavior.
publishDate 2012
dc.date.none.fl_str_mv 2012-01
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/11336/19945
Groisman, Pablo Jose; Saglietti, Santiago Juan; Small random perturbations of a dynamical system with blow-up; Elsevier Inc; Journal Of Mathematical Analysis And Applications; 385; 1; 1-2012; 150-166
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19945
identifier_str_mv Groisman, Pablo Jose; Saglietti, Santiago Juan; Small random perturbations of a dynamical system with blow-up; Elsevier Inc; Journal Of Mathematical Analysis And Applications; 385; 1; 1-2012; 150-166
0022-247X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2011.06.034
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X11005828
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1011.3414
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Inc
publisher.none.fl_str_mv Elsevier Inc
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
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score 13.070432

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