On a p-curl system arising in electromagnetism

Bibliographic Details
Main Author: Miranda, Fernando
Publication Date: 2012
Other Authors: Rodrigues, José Francisco, Santos, Lisa
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/1822/17881
Summary: We prove existence of solution of a $p$-curl type evolutionary system arising in electromagnetism with a power nonlinearity of order $p$, $1<p<\infty$, assuming natural tangential boundary conditions. We consider also the asymptotic behaviour in the power obtaining, when $p$ tends to infinity, a variational inequality with a curl constraint. We also discuss the existence, uniqueness and continuous dependence on the data of the solutions to general variational inequalities with curl constraints dependent on time, as well as the asymptotic stabilization in time towards the stationary solution with and without constraint.
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spelling On a p-curl system arising in electromagnetismElectromagnetic problemsVariational methodsVariational inequalitiesSuperconductivity modelsElectromagnetic problems; variational methodsScience & TechnologyWe prove existence of solution of a $p$-curl type evolutionary system arising in electromagnetism with a power nonlinearity of order $p$, $1<p<\infty$, assuming natural tangential boundary conditions. We consider also the asymptotic behaviour in the power obtaining, when $p$ tends to infinity, a variational inequality with a curl constraint. We also discuss the existence, uniqueness and continuous dependence on the data of the solutions to general variational inequalities with curl constraints dependent on time, as well as the asymptotic stabilization in time towards the stationary solution with and without constraint.The first an last authors are supported by the Research Centre of Mathematics of the University of Minho through the FCT Pluriannual Funding Program and FCT project UT-Austin/MAT/0035/2008.American Institute of Mathematical Sciences (AIMS)Universidade do MinhoMiranda, FernandoRodrigues, José FranciscoSantos, Lisa2012-062012-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/17881eng1937-1632 (print)10.3934/dcdss.2012.5.605http://dx.doi.org/10.3934/dcdss.2012.5.605info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-11T04:16:12Zoai:repositorium.sdum.uminho.pt:1822/17881Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:43:48.721851Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv On a p-curl system arising in electromagnetism
title On a p-curl system arising in electromagnetism
spellingShingle On a p-curl system arising in electromagnetism
Miranda, Fernando
Electromagnetic problems
Variational methods
Variational inequalities
Superconductivity models
Electromagnetic problems; variational methods
Science & Technology
title_short On a p-curl system arising in electromagnetism
title_full On a p-curl system arising in electromagnetism
title_fullStr On a p-curl system arising in electromagnetism
title_full_unstemmed On a p-curl system arising in electromagnetism
title_sort On a p-curl system arising in electromagnetism
author Miranda, Fernando
author_facet Miranda, Fernando
Rodrigues, José Francisco
Santos, Lisa
author_role author
author2 Rodrigues, José Francisco
Santos, Lisa
author2_role author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Miranda, Fernando
Rodrigues, José Francisco
Santos, Lisa
dc.subject.por.fl_str_mv Electromagnetic problems
Variational methods
Variational inequalities
Superconductivity models
Electromagnetic problems; variational methods
Science & Technology
topic Electromagnetic problems
Variational methods
Variational inequalities
Superconductivity models
Electromagnetic problems; variational methods
Science & Technology
description We prove existence of solution of a $p$-curl type evolutionary system arising in electromagnetism with a power nonlinearity of order $p$, $1<p<\infty$, assuming natural tangential boundary conditions. We consider also the asymptotic behaviour in the power obtaining, when $p$ tends to infinity, a variational inequality with a curl constraint. We also discuss the existence, uniqueness and continuous dependence on the data of the solutions to general variational inequalities with curl constraints dependent on time, as well as the asymptotic stabilization in time towards the stationary solution with and without constraint.
publishDate 2012
dc.date.none.fl_str_mv 2012-06
2012-06-01T00:00:00Z
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/1822/17881
url http://hdl.handle.net/1822/17881
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1937-1632 (print)
10.3934/dcdss.2012.5.605
http://dx.doi.org/10.3934/dcdss.2012.5.605
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833594848533282816

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