On the controllability of parabolic systems with a nonlinear term involving the state and the gradient

We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of RN with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary cont...

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Detalles Bibliográficos
Autores: Doubova Krasotchenko, Anna, Fernández Cara, Enrique, González Burgos, Manuel, Zuazua Iriondo, Enrique
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2002
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41189
Acceso en línea:http://hdl.handle.net/11441/41189
https://doi.org/10.1137/S0363012901386465
Access Level:acceso abierto
Palabra clave:Controllability
Parabolic equations
Nonlinear gradient terms
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spelling On the controllability of parabolic systems with a nonlinear term involving the state and the gradientDoubova Krasotchenko, AnnaFernández Cara, EnriqueGonzález Burgos, ManuelZuazua Iriondo, EnriqueControllabilityParabolic equationsNonlinear gradient termsWe present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of RN with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term f(y, ∇y) grows slower than |y| log3/2(1+ |y|+ |∇y|)+ |∇y| log1/2(1+ |y|+ |∇y|) at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method.Ministerio de Educación y CienciaSociety for Industrial and Applied MathematicsEcuaciones Diferenciales y Análisis NuméricoMinisterio de Educación y Ciencia (MEC). España2002info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41189https://doi.org/10.1137/S0363012901386465reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésnullPB96-0663PB98-1134BFM2000-1317http://dx.doi.org/10.1137/S0363012901386465info:eu-repo/semantics/openAccessoai:idus.us.es:11441/411892026-06-17T12:51:07Z
dc.title.none.fl_str_mv On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
title On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
spellingShingle On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
Doubova Krasotchenko, Anna
Controllability
Parabolic equations
Nonlinear gradient terms
title_short On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
title_full On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
title_fullStr On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
title_full_unstemmed On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
title_sort On the controllability of parabolic systems with a nonlinear term involving the state and the gradient
dc.creator.none.fl_str_mv Doubova Krasotchenko, Anna
Fernández Cara, Enrique
González Burgos, Manuel
Zuazua Iriondo, Enrique
author Doubova Krasotchenko, Anna
author_facet Doubova Krasotchenko, Anna
Fernández Cara, Enrique
González Burgos, Manuel
Zuazua Iriondo, Enrique
author_role author
author2 Fernández Cara, Enrique
González Burgos, Manuel
Zuazua Iriondo, Enrique
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
Ministerio de Educación y Ciencia (MEC). España
dc.subject.none.fl_str_mv Controllability
Parabolic equations
Nonlinear gradient terms
topic Controllability
Parabolic equations
Nonlinear gradient terms
description We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of RN with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term f(y, ∇y) grows slower than |y| log3/2(1+ |y|+ |∇y|)+ |∇y| log1/2(1+ |y|+ |∇y|) at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method.
publishDate 2002
dc.date.none.fl_str_mv 2002
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/41189
https://doi.org/10.1137/S0363012901386465
url http://hdl.handle.net/11441/41189
https://doi.org/10.1137/S0363012901386465
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv null
PB96-0663
PB98-1134
BFM2000-1317
http://dx.doi.org/10.1137/S0363012901386465
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
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