Approximate controllability for the semilinear heat equation in R N involving gradient terms

Detalhes bibliográficos
Autor(a) principal: Menezes,Silvano Bezerra de
Data de Publicação: 2003
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100008
Resumo: We prove the approximate controllability of the semilinear heat equation in R N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient <FONT FACE=Symbol>Ñ</FONT>u. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces.
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spelling Approximate controllability for the semilinear heat equation in R N involving gradient termsapproximate controllabilityoptimal controlunbounded domainsweighted Sobolev spacesWe prove the approximate controllability of the semilinear heat equation in R N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient <FONT FACE=Symbol>Ñ</FONT>u. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces.Sociedade Brasileira de Matemática Aplicada e Computacional2003-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100008Computational &amp; Applied Mathematics v.22 n.1 2003reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMACinfo:eu-repo/semantics/openAccessMenezes,Silvano Bezerra deeng2004-07-19T00:00:00Zoai:scielo:S1807-03022003000100008Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2004-07-19T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv Approximate controllability for the semilinear heat equation in R N involving gradient terms
title Approximate controllability for the semilinear heat equation in R N involving gradient terms
spellingShingle Approximate controllability for the semilinear heat equation in R N involving gradient terms
Menezes,Silvano Bezerra de
approximate controllability
optimal control
unbounded domains
weighted Sobolev spaces
title_short Approximate controllability for the semilinear heat equation in R N involving gradient terms
title_full Approximate controllability for the semilinear heat equation in R N involving gradient terms
title_fullStr Approximate controllability for the semilinear heat equation in R N involving gradient terms
title_full_unstemmed Approximate controllability for the semilinear heat equation in R N involving gradient terms
title_sort Approximate controllability for the semilinear heat equation in R N involving gradient terms
author Menezes,Silvano Bezerra de
author_facet Menezes,Silvano Bezerra de
author_role author
dc.contributor.author.fl_str_mv Menezes,Silvano Bezerra de
dc.subject.por.fl_str_mv approximate controllability
optimal control
unbounded domains
weighted Sobolev spaces
topic approximate controllability
optimal control
unbounded domains
weighted Sobolev spaces
description We prove the approximate controllability of the semilinear heat equation in R N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient <FONT FACE=Symbol>Ñ</FONT>u. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces.
publishDate 2003
dc.date.none.fl_str_mv 2003-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100008
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational &amp; Applied Mathematics v.22 n.1 2003
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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