Well-posedness of KdV type equations

Detalhes bibliográficos
Autor(a) principal: Carvajal, Xavier
Data de Publicação: 2012
Outros Autores: Panthee, Mahendra Prasad
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/17877
Resumo: In this work, we study the initial value problems associated to some linear perturbations of the KdV equations. Our focus is in the well-posedness issues for the initial data given in the $L^2$-based Sobolev spaces. We develop a method that allows us to treat the problem in the Bourgain's space associated to the KdV equation. With this method, we can use the multilinear estimates developed in the KdV context thereby getting analogous well-posedness results for the linearly perturbed equations.
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spelling Well-posedness of KdV type equationsInitial value problemwell-posednessBourgain spacesKdV equationScience & TechnologyIn this work, we study the initial value problems associated to some linear perturbations of the KdV equations. Our focus is in the well-posedness issues for the initial data given in the $L^2$-based Sobolev spaces. We develop a method that allows us to treat the problem in the Bourgain's space associated to the KdV equation. With this method, we can use the multilinear estimates developed in the KdV context thereby getting analogous well-posedness results for the linearly perturbed equations.Fundação para a Ciência e a Tecnologia (FCT)Texas State University. Department of MathematicsUniversidade do MinhoCarvajal, XavierPanthee, Mahendra Prasad20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/17877eng1072-6691http://ejde.math.txstate.edu/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:RCAAP2023-07-21T12:37:14Zoai:repositorium.sdum.uminho.pt:1822/17877Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:33:29.748274Repositório 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 Well-posedness of KdV type equations
title Well-posedness of KdV type equations
spellingShingle Well-posedness of KdV type equations
Carvajal, Xavier
Initial value problem
well-posedness
Bourgain spaces
KdV equation
Science & Technology
title_short Well-posedness of KdV type equations
title_full Well-posedness of KdV type equations
title_fullStr Well-posedness of KdV type equations
title_full_unstemmed Well-posedness of KdV type equations
title_sort Well-posedness of KdV type equations
author Carvajal, Xavier
author_facet Carvajal, Xavier
Panthee, Mahendra Prasad
author_role author
author2 Panthee, Mahendra Prasad
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Carvajal, Xavier
Panthee, Mahendra Prasad
dc.subject.por.fl_str_mv Initial value problem
well-posedness
Bourgain spaces
KdV equation
Science & Technology
topic Initial value problem
well-posedness
Bourgain spaces
KdV equation
Science & Technology
description In this work, we study the initial value problems associated to some linear perturbations of the KdV equations. Our focus is in the well-posedness issues for the initial data given in the $L^2$-based Sobolev spaces. We develop a method that allows us to treat the problem in the Bourgain's space associated to the KdV equation. With this method, we can use the multilinear estimates developed in the KdV context thereby getting analogous well-posedness results for the linearly perturbed equations.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01T00:00:00Z
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/1822/17877
url http://hdl.handle.net/1822/17877
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1072-6691
http://ejde.math.txstate.edu/
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 Texas State University. Department of Mathematics
publisher.none.fl_str_mv Texas State University. Department of Mathematics
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
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instacron_str RCAAP
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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
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