A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time

Autores
Tertuliano, Franco; Groisman, Pablo Jose
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation ∂tu = ∂xxu + f(u). If f(u) = u p , 1 < p ≤ 3, we also obtain a law of large numbers for the explosion time.
Fil: Tertuliano, Franco. Universidade Federal Da Bahia; Brasil
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
Materia
Hydrodinamic Limit
Blow-Up
Reaction-Diffusion Equation
Particle System
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:11336/19892
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up TimeTertuliano, FrancoGroisman, Pablo JoseHydrodinamic LimitBlow-UpReaction-Diffusion EquationParticle Systemhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation ∂tu = ∂xxu + f(u). If f(u) = u p , 1 < p ≤ 3, we also obtain a law of large numbers for the explosion time.Fil: Tertuliano, Franco. Universidade Federal Da Bahia; BrasilFil: 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"; ArgentinaSpringer2012-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19892Tertuliano, Franco; Groisman, Pablo Jose; A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time; Springer; Journal Of Statistical Physics; 149; 4; 11-2012; 629-6420022-47151572-9613CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10955-012-0621-8info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10955-012-0621-8info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1207.1574info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:15:07Zoai:ri.conicet.gov.ar:11336/19892instacron: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:34982025-10-22 11:15:08.097CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
spellingShingle A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
Tertuliano, Franco
Hydrodinamic Limit
Blow-Up
Reaction-Diffusion Equation
Particle System
title_short A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_full A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_fullStr A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_full_unstemmed A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_sort A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
dc.creator.none.fl_str_mv Tertuliano, Franco
Groisman, Pablo Jose
author Tertuliano, Franco
author_facet Tertuliano, Franco
Groisman, Pablo Jose
author_role author
author2 Groisman, Pablo Jose
author2_role author
dc.subject.none.fl_str_mv Hydrodinamic Limit
Blow-Up
Reaction-Diffusion Equation
Particle System
topic Hydrodinamic Limit
Blow-Up
Reaction-Diffusion Equation
Particle System
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation ∂tu = ∂xxu + f(u). If f(u) = u p , 1 < p ≤ 3, we also obtain a law of large numbers for the explosion time.
Fil: Tertuliano, Franco. Universidade Federal Da Bahia; Brasil
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
description Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation ∂tu = ∂xxu + f(u). If f(u) = u p , 1 < p ≤ 3, we also obtain a law of large numbers for the explosion time.
publishDate 2012
dc.date.none.fl_str_mv 2012-11
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/11336/19892
Tertuliano, Franco; Groisman, Pablo Jose; A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time; Springer; Journal Of Statistical Physics; 149; 4; 11-2012; 629-642
0022-4715
1572-9613
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19892
identifier_str_mv Tertuliano, Franco; Groisman, Pablo Jose; A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time; Springer; Journal Of Statistical Physics; 149; 4; 11-2012; 629-642
0022-4715
1572-9613
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10955-012-0621-8
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10955-012-0621-8
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1207.1574
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 Springer
publisher.none.fl_str_mv Springer
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 12.982451

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