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

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

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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Main Author: Menezes,Silvano Bezerra de
Format: Digital revista
Language:English
Published: Sociedade Brasileira de Matemática Aplicada e Computacional 2003
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100008
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spelling oai:scielo:S1807-030220030001000082004-07-19Approximate controllability for the semilinear heat equation in R N involving gradient termsMenezes,Silvano Bezerra de approximate controllability optimal control unbounded domains weighted Sobolev spaces 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.info:eu-repo/semantics/openAccessSociedade Brasileira de Matemática Aplicada e ComputacionalComputational &amp; Applied Mathematics v.22 n.1 20032003-01-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100008en
institution SCIELO
collection OJS
country Brasil
countrycode BR
component Revista
access En linea
databasecode rev-scielo-br
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author Menezes,Silvano Bezerra de
spellingShingle Menezes,Silvano Bezerra de
Approximate controllability for the semilinear heat equation in R N involving gradient terms
author_facet Menezes,Silvano Bezerra de
author_sort Menezes,Silvano Bezerra de
title Approximate controllability for the semilinear heat equation in R N involving gradient terms
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
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.
publisher Sociedade Brasileira de Matemática Aplicada e Computacional
publishDate 2003
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100008
work_keys_str_mv AT menezessilvanobezerrade approximatecontrollabilityforthesemilinearheatequationinrninvolvinggradientterms
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