Phase transition of a heat equation with Robin's boundary conditions and exclusion process

Detalhes bibliográficos
Autor(a) principal: Gonçalves, Patrícia
Data de Publicação: 2015
Outros Autores: Franco, Tertuliano, Neumann, Adriana
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/23518
Resumo: For a heat equation with Robin's boundary conditions which depends on a parameter $\alpha>0$, we prove that its unique weak solution $\rho^\alpha$ converges, when $\alpha$ goes to zero or to infinity, to the unique weak solution of the heat equation with Neumann's boundary conditions or the heat equation with periodic boundary conditions, respectively. To this end, we use uniform bounds on a Sobolev norm of $\rho^\alpha$ obtained from the hydrodynamic limit of the symmetric slowed exclusion process, plus a careful analysis of boundary terms.
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spelling Phase transition of a heat equation with Robin's boundary conditions and exclusion processSlowed exclusionPhase transitionHeat equationRobin's boundary conditionsHydrodynamic limitHydrodynamicLimitRobin boundary conditionsScience & TechnologyFor a heat equation with Robin's boundary conditions which depends on a parameter $\alpha>0$, we prove that its unique weak solution $\rho^\alpha$ converges, when $\alpha$ goes to zero or to infinity, to the unique weak solution of the heat equation with Neumann's boundary conditions or the heat equation with periodic boundary conditions, respectively. To this end, we use uniform bounds on a Sobolev norm of $\rho^\alpha$ obtained from the hydrodynamic limit of the symmetric slowed exclusion process, plus a careful analysis of boundary terms.FCTCAPESAmerican Mathematical SocietyUniversidade do MinhoGonçalves, PatríciaFranco, TertulianoNeumann, Adriana20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/23518engFranco, T., Gonçalves, P., & Neumann, A. (2015). Phase transition of a heat equation with Robin’s boundary conditions and exclusion process. Transactions of the American Mathematical Society, 367(9), 6131-6158.0002-9947http://www.ams.org/publications/journals/journalsframework/traninfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:49:53Zoai:repositorium.sdum.uminho.pt:1822/23518Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:48:29.043213Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Phase transition of a heat equation with Robin's boundary conditions and exclusion process
title Phase transition of a heat equation with Robin's boundary conditions and exclusion process
spellingShingle Phase transition of a heat equation with Robin's boundary conditions and exclusion process
Gonçalves, Patrícia
Slowed exclusion
Phase transition
Heat equation
Robin's boundary conditions
Hydrodynamic limit
Hydrodynamic
Limit
Robin boundary conditions
Science & Technology
title_short Phase transition of a heat equation with Robin's boundary conditions and exclusion process
title_full Phase transition of a heat equation with Robin's boundary conditions and exclusion process
title_fullStr Phase transition of a heat equation with Robin's boundary conditions and exclusion process
title_full_unstemmed Phase transition of a heat equation with Robin's boundary conditions and exclusion process
title_sort Phase transition of a heat equation with Robin's boundary conditions and exclusion process
author Gonçalves, Patrícia
author_facet Gonçalves, Patrícia
Franco, Tertuliano
Neumann, Adriana
author_role author
author2 Franco, Tertuliano
Neumann, Adriana
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Gonçalves, Patrícia
Franco, Tertuliano
Neumann, Adriana
dc.subject.por.fl_str_mv Slowed exclusion
Phase transition
Heat equation
Robin's boundary conditions
Hydrodynamic limit
Hydrodynamic
Limit
Robin boundary conditions
Science & Technology
topic Slowed exclusion
Phase transition
Heat equation
Robin's boundary conditions
Hydrodynamic limit
Hydrodynamic
Limit
Robin boundary conditions
Science & Technology
description For a heat equation with Robin's boundary conditions which depends on a parameter $\alpha>0$, we prove that its unique weak solution $\rho^\alpha$ converges, when $\alpha$ goes to zero or to infinity, to the unique weak solution of the heat equation with Neumann's boundary conditions or the heat equation with periodic boundary conditions, respectively. To this end, we use uniform bounds on a Sobolev norm of $\rho^\alpha$ obtained from the hydrodynamic limit of the symmetric slowed exclusion process, plus a careful analysis of boundary terms.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1822/23518
url http://hdl.handle.net/1822/23518
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Franco, T., Gonçalves, P., & Neumann, A. (2015). Phase transition of a heat equation with Robin’s boundary conditions and exclusion process. Transactions of the American Mathematical Society, 367(9), 6131-6158.
0002-9947
http://www.ams.org/publications/journals/journalsframework/tran
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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