Approximate controllability for the semilinear heat equation in RN involving gradient terms

Detalhes bibliográficos
Autor(a) principal: MENEZES, Silvano Dias Bezerra de
Data de Publicação: 2003
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFPA
Texto Completo: http://repositorio.ufpa.br/jspui/handle/2011/6161
Resumo: We prove the approximate controllability of the semilinear heat equation in RN, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. 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 2014-12-15T16:28:42Z2014-12-15T16:28:42Z2003MENEZES, Silvano Bezerra de. Approximate controllability for the semilinear heat equation in RN involving gradient terms. Computational & Applied Mathematics, São Carlos, v. 22, n. 1, p. 123-148, 2003. Disponível em: <http://www.scielo.br/pdf/cam/v22n1/08v22n1.pdf>. Acesso em: 28 nov. 2014.1807-0302http://repositorio.ufpa.br/jspui/handle/2011/6161We prove the approximate controllability of the semilinear heat equation in RN, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. 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.engEquação diferencial elipticaEquação diferencial não-linearEquação de calorControlabilidade aproximada finitaEspaço de SobolevApproximate controllability for the semilinear heat equation in RN involving gradient termsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleMENEZES, Silvano Dias Bezerra deinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFPAinstname:Universidade Federal do Pará (UFPA)instacron:UFPAORIGINALArtigo_ApproximateControllabilitySemilinear.pdfArtigo_ApproximateControllabilitySemilinear.pdfapplication/pdf169049http://repositorio.ufpa.br/oai/bitstream/2011/6161/1/Artigo_ApproximateControllabilitySemilinear.pdf81843973490e1cce11cb2225818e2e02MD51CC-LICENSElicense_urllicense_urltext/plain; charset=utf-849http://repositorio.ufpa.br/oai/bitstream/2011/6161/2/license_url4afdbb8c545fd630ea7db775da747b2fMD52license_textlicense_texttext/html; charset=utf-822302http://repositorio.ufpa.br/oai/bitstream/2011/6161/3/license_text1e0094e9d8adcf16b18effef4ce7ed83MD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-823148http://repositorio.ufpa.br/oai/bitstream/2011/6161/4/license_rdf9da0b6dfac957114c6a7714714b86306MD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81771http://repositorio.ufpa.br/oai/bitstream/2011/6161/5/license.txt8d4b53618491f2f87a6f781e9656086cMD55TEXTArtigo_ApproximateControllabilitySemilinear.pdf.txtArtigo_ApproximateControllabilitySemilinear.pdf.txtExtracted texttext/plain41411http://repositorio.ufpa.br/oai/bitstream/2011/6161/6/Artigo_ApproximateControllabilitySemilinear.pdf.txt60b4e21d0d425b877e35e2b2a1d45d0bMD562011/61612017-12-22 11:46:30.12oai:repositorio.ufpa.br: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Repositório InstitucionalPUBhttp://repositorio.ufpa.br/oai/requestriufpabc@ufpa.bropendoar:21232017-12-22T14:46:30Repositório Institucional da UFPA - Universidade Federal do Pará (UFPA)false
dc.title.pt_BR.fl_str_mv Approximate controllability for the semilinear heat equation in RN involving gradient terms
title Approximate controllability for the semilinear heat equation in RN involving gradient terms
spellingShingle Approximate controllability for the semilinear heat equation in RN involving gradient terms
MENEZES, Silvano Dias Bezerra de
Equação diferencial eliptica
Equação diferencial não-linear
Equação de calor
Controlabilidade aproximada finita
Espaço de Sobolev
title_short Approximate controllability for the semilinear heat equation in RN involving gradient terms
title_full Approximate controllability for the semilinear heat equation in RN involving gradient terms
title_fullStr Approximate controllability for the semilinear heat equation in RN involving gradient terms
title_full_unstemmed Approximate controllability for the semilinear heat equation in RN involving gradient terms
title_sort Approximate controllability for the semilinear heat equation in RN involving gradient terms
author MENEZES, Silvano Dias Bezerra de
author_facet MENEZES, Silvano Dias Bezerra de
author_role author
dc.contributor.author.fl_str_mv MENEZES, Silvano Dias Bezerra de
dc.subject.por.fl_str_mv Equação diferencial eliptica
Equação diferencial não-linear
Equação de calor
Controlabilidade aproximada finita
Espaço de Sobolev
topic Equação diferencial eliptica
Equação diferencial não-linear
Equação de calor
Controlabilidade aproximada finita
Espaço de Sobolev
description We prove the approximate controllability of the semilinear heat equation in RN, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient Ñu. 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.issued.fl_str_mv 2003
dc.date.accessioned.fl_str_mv 2014-12-15T16:28:42Z
dc.date.available.fl_str_mv 2014-12-15T16:28:42Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.citation.fl_str_mv MENEZES, Silvano Bezerra de. Approximate controllability for the semilinear heat equation in RN involving gradient terms. Computational & Applied Mathematics, São Carlos, v. 22, n. 1, p. 123-148, 2003. Disponível em: <http://www.scielo.br/pdf/cam/v22n1/08v22n1.pdf>. Acesso em: 28 nov. 2014.
dc.identifier.uri.fl_str_mv http://repositorio.ufpa.br/jspui/handle/2011/6161
dc.identifier.issn.none.fl_str_mv 1807-0302
identifier_str_mv MENEZES, Silvano Bezerra de. Approximate controllability for the semilinear heat equation in RN involving gradient terms. Computational & Applied Mathematics, São Carlos, v. 22, n. 1, p. 123-148, 2003. Disponível em: <http://www.scielo.br/pdf/cam/v22n1/08v22n1.pdf>. Acesso em: 28 nov. 2014.
1807-0302
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dc.language.iso.fl_str_mv eng
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