Metastability for small random perturbations of a PDE with blow-up

Autores
Groisman, Pablo Jose; Saglietti, Santiago Juan; Saintier, Nicolas Bernard Claude
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study random perturbations of a reaction–diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation ε>0 is small and the initial data is in the domain of attraction of the stable equilibrium, the system exhibits metastable behavior: its time averages remain stable around this equilibrium until an abrupt and unpredictable transition occurs which leads to explosion in a finite time (but exponentially large in ε−2). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution.
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. NYU Shanghai. Institute of Mathematical Sciences; China
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. Technion - Israel Institute of Technology; Israel
Fil: Saintier, Nicolas Bernard Claude. 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
RANDOM PERTURBATIONS
STOCHASTIC PARTIAL 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:11336/60062
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Metastability for small random perturbations of a PDE with blow-upGroisman, Pablo JoseSaglietti, Santiago JuanSaintier, Nicolas Bernard ClaudeBLOW-UPMETASTABILITYRANDOM PERTURBATIONSSTOCHASTIC PARTIAL DIFFERENTIAL EQUATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study random perturbations of a reaction–diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation ε>0 is small and the initial data is in the domain of attraction of the stable equilibrium, the system exhibits metastable behavior: its time averages remain stable around this equilibrium until an abrupt and unpredictable transition occurs which leads to explosion in a finite time (but exponentially large in ε−2). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution.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. NYU Shanghai. Institute of Mathematical Sciences; ChinaFil: 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. Technion - Israel Institute of Technology; IsraelFil: Saintier, Nicolas Bernard Claude. 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 Science2018-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60062Groisman, Pablo Jose; Saglietti, Santiago Juan; Saintier, Nicolas Bernard Claude; Metastability for small random perturbations of a PDE with blow-up; Elsevier Science; Stochastic Processes And Their Applications; 128; 5; 5-2018; 1558-15890304-4149CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.spa.2017.08.005info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0304414917301965info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1501.01724info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:35:01Zoai:ri.conicet.gov.ar:11336/60062instacron: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:34982025-11-12 09:35:02.091CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Metastability for small random perturbations of a PDE with blow-up
title Metastability for small random perturbations of a PDE with blow-up
spellingShingle Metastability for small random perturbations of a PDE with blow-up
Groisman, Pablo Jose
BLOW-UP
METASTABILITY
RANDOM PERTURBATIONS
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
title_short Metastability for small random perturbations of a PDE with blow-up
title_full Metastability for small random perturbations of a PDE with blow-up
title_fullStr Metastability for small random perturbations of a PDE with blow-up
title_full_unstemmed Metastability for small random perturbations of a PDE with blow-up
title_sort Metastability for small random perturbations of a PDE with blow-up
dc.creator.none.fl_str_mv Groisman, Pablo Jose
Saglietti, Santiago Juan
Saintier, Nicolas Bernard Claude
author Groisman, Pablo Jose
author_facet Groisman, Pablo Jose
Saglietti, Santiago Juan
Saintier, Nicolas Bernard Claude
author_role author
author2 Saglietti, Santiago Juan
Saintier, Nicolas Bernard Claude
author2_role author
author
dc.subject.none.fl_str_mv BLOW-UP
METASTABILITY
RANDOM PERTURBATIONS
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
topic BLOW-UP
METASTABILITY
RANDOM PERTURBATIONS
STOCHASTIC PARTIAL 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 random perturbations of a reaction–diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation ε>0 is small and the initial data is in the domain of attraction of the stable equilibrium, the system exhibits metastable behavior: its time averages remain stable around this equilibrium until an abrupt and unpredictable transition occurs which leads to explosion in a finite time (but exponentially large in ε−2). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution.
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. NYU Shanghai. Institute of Mathematical Sciences; China
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. Technion - Israel Institute of Technology; Israel
Fil: Saintier, Nicolas Bernard Claude. 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 random perturbations of a reaction–diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation ε>0 is small and the initial data is in the domain of attraction of the stable equilibrium, the system exhibits metastable behavior: its time averages remain stable around this equilibrium until an abrupt and unpredictable transition occurs which leads to explosion in a finite time (but exponentially large in ε−2). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution.
publishDate 2018
dc.date.none.fl_str_mv 2018-05
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/11336/60062
Groisman, Pablo Jose; Saglietti, Santiago Juan; Saintier, Nicolas Bernard Claude; Metastability for small random perturbations of a PDE with blow-up; Elsevier Science; Stochastic Processes And Their Applications; 128; 5; 5-2018; 1558-1589
0304-4149
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60062
identifier_str_mv Groisman, Pablo Jose; Saglietti, Santiago Juan; Saintier, Nicolas Bernard Claude; Metastability for small random perturbations of a PDE with blow-up; Elsevier Science; Stochastic Processes And Their Applications; 128; 5; 5-2018; 1558-1589
0304-4149
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.spa.2017.08.005
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0304414917301965
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1501.01724
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
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 12.976206

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