On the ill-posedness result for the BBM equation

Detalhes bibliográficos
Autor(a) principal: Panthee, Mahendra Prasad
Data de Publicação: 2011
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/13473
Resumo: We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hs(R), s < 0 in the sense that the ow-map u0 7! u(t) that associates to initial data u0 the solution u cannot be continuous at the origin from Hs(R) to even D0(R) at any _xed t > 0 small enough. This result is sharp.
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spelling On the ill-posedness result for the BBM equationCauchy problemWell-posednessIll-posednessKdV equationBBM equationScience & TechnologyWe prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hs(R), s < 0 in the sense that the ow-map u0 7! u(t) that associates to initial data u0 the solution u cannot be continuous at the origin from Hs(R) to even D0(R) at any _xed t > 0 small enough. This result is sharp.Fundação para a Ciência e a Tecnologia (FCT)American Institute of Mathematical Sciences (AIMS)Universidade do MinhoPanthee, Mahendra Prasad2011-052011-05-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/13473eng1078-094710.3934/dcds.2011.30.253http://www.aimsciences.org/info: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:RCAAP2023-07-21T12:41:09Zoai:repositorium.sdum.uminho.pt:1822/13473Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:38:04.589490Repositório 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 On the ill-posedness result for the BBM equation
title On the ill-posedness result for the BBM equation
spellingShingle On the ill-posedness result for the BBM equation
Panthee, Mahendra Prasad
Cauchy problem
Well-posedness
Ill-posedness
KdV equation
BBM equation
Science & Technology
title_short On the ill-posedness result for the BBM equation
title_full On the ill-posedness result for the BBM equation
title_fullStr On the ill-posedness result for the BBM equation
title_full_unstemmed On the ill-posedness result for the BBM equation
title_sort On the ill-posedness result for the BBM equation
author Panthee, Mahendra Prasad
author_facet Panthee, Mahendra Prasad
author_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Panthee, Mahendra Prasad
dc.subject.por.fl_str_mv Cauchy problem
Well-posedness
Ill-posedness
KdV equation
BBM equation
Science & Technology
topic Cauchy problem
Well-posedness
Ill-posedness
KdV equation
BBM equation
Science & Technology
description We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hs(R), s < 0 in the sense that the ow-map u0 7! u(t) that associates to initial data u0 the solution u cannot be continuous at the origin from Hs(R) to even D0(R) at any _xed t > 0 small enough. This result is sharp.
publishDate 2011
dc.date.none.fl_str_mv 2011-05
2011-05-01T00:00:00Z
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/1822/13473
url http://hdl.handle.net/1822/13473
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1078-0947
10.3934/dcds.2011.30.253
http://www.aimsciences.org/
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 Institute of Mathematical Sciences (AIMS)
publisher.none.fl_str_mv American Institute of Mathematical Sciences (AIMS)
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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