A nonlinear hyperbolic Maxwell system using measure-valued functions

Detalhes bibliográficos
Autor(a) principal: Miranda, Fernando
Data de Publicação: 2012
Outros Autores: Santos, Lisa
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/13589
Resumo: We consider a modified antenna's problem with power-type constitutive laws. This consists in a new nonlinear hyperbolic system that extends a Duvaut-Lions model. Using the Galerkin approximation, properties of the natural functional spaces, and exploring the $L^p$-$L^{p'}$ duality, we prove the existence of solutions, in a generalized sense, passing to the limit in a family of approximated problems and using measure-valued functions. In this process the difficulties in obtaining the necessary a priori estimates for the solutions of the finite-dimensional problems are overcome through the use of bases with special properties related to the model.
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spelling A nonlinear hyperbolic Maxwell system using measure-valued functionsHyperbolic systemMeasure-valued functionsDuality L(p)-L(p)'Duality L -L ' p pScience & TechnologyWe consider a modified antenna's problem with power-type constitutive laws. This consists in a new nonlinear hyperbolic system that extends a Duvaut-Lions model. Using the Galerkin approximation, properties of the natural functional spaces, and exploring the $L^p$-$L^{p'}$ duality, we prove the existence of solutions, in a generalized sense, passing to the limit in a family of approximated problems and using measure-valued functions. In this process the difficulties in obtaining the necessary a priori estimates for the solutions of the finite-dimensional problems are overcome through the use of bases with special properties related to the model.The research of the authors was partially supported by the Research Centre of Mathematics of the University of Minho through the FCT Pluriannual Funding Program.ElsevierUniversidade do MinhoMiranda, FernandoSantos, Lisa2012-01-012012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/13589eng0022-247X10.1016/j.jmaa.2011.06.071info: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:RCAAP2023-07-21T12:37:58Zoai:repositorium.sdum.uminho.pt:1822/13589Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:34:19.496582Repositório 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 A nonlinear hyperbolic Maxwell system using measure-valued functions
title A nonlinear hyperbolic Maxwell system using measure-valued functions
spellingShingle A nonlinear hyperbolic Maxwell system using measure-valued functions
Miranda, Fernando
Hyperbolic system
Measure-valued functions
Duality L(p)-L(p)'
Duality L -L ' p p
Science & Technology
title_short A nonlinear hyperbolic Maxwell system using measure-valued functions
title_full A nonlinear hyperbolic Maxwell system using measure-valued functions
title_fullStr A nonlinear hyperbolic Maxwell system using measure-valued functions
title_full_unstemmed A nonlinear hyperbolic Maxwell system using measure-valued functions
title_sort A nonlinear hyperbolic Maxwell system using measure-valued functions
author Miranda, Fernando
author_facet Miranda, Fernando
Santos, Lisa
author_role author
author2 Santos, Lisa
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Miranda, Fernando
Santos, Lisa
dc.subject.por.fl_str_mv Hyperbolic system
Measure-valued functions
Duality L(p)-L(p)'
Duality L -L ' p p
Science & Technology
topic Hyperbolic system
Measure-valued functions
Duality L(p)-L(p)'
Duality L -L ' p p
Science & Technology
description We consider a modified antenna's problem with power-type constitutive laws. This consists in a new nonlinear hyperbolic system that extends a Duvaut-Lions model. Using the Galerkin approximation, properties of the natural functional spaces, and exploring the $L^p$-$L^{p'}$ duality, we prove the existence of solutions, in a generalized sense, passing to the limit in a family of approximated problems and using measure-valued functions. In this process the difficulties in obtaining the necessary a priori estimates for the solutions of the finite-dimensional problems are overcome through the use of bases with special properties related to the model.
publishDate 2012
dc.date.none.fl_str_mv 2012-01-01
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/1822/13589
url http://hdl.handle.net/1822/13589
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-247X
10.1016/j.jmaa.2011.06.071
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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