Approximate controllability for the semilinear heat equation in R N involving gradient terms
Autor(a) principal: | |
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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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Computational & Applied Mathematics |
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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 & 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 |
format |
article |
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 & 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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1754734889657171968 |