Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity

In this paper we consider a semilinear heat equation (in a bounded domain Ω of IRN ) with a nonlinearity that has a superlinear growth at infinity. We prove the existence of a control, with support in an open set ω ⊂ Ω, that insensitizes the L2−norm of the observation of the solution in another open...

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Autores: Bodart, Olivier, González Burgos, Manuel, Pérez García, Rosario
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2004
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41481
Acceso en línea:http://hdl.handle.net/11441/41481
https://doi.org/10.1081/PDE-200033749
Access Level:acceso abierto
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spelling Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearityBodart, OlivierGonzález Burgos, ManuelPérez García, RosarioIn this paper we consider a semilinear heat equation (in a bounded domain Ω of IRN ) with a nonlinearity that has a superlinear growth at infinity. We prove the existence of a control, with support in an open set ω ⊂ Ω, that insensitizes the L2−norm of the observation of the solution in another open subset O ⊂ Ω when ω ∩ O 6= ∅, under suitable assumptions on the nonlinear term f(y) and the right hand side term ξ of the equation. The proof, involving global Carleman estimates and regularizing properties of the heat equation, relies on the sharp study of a similar linearized problem and an appropriate fixed-point argument. For certain superlinear nonlinearities, we also prove an insensitivity result of a negative nature. The crucial point in this paper is the technique of construction of L r–controls (r large enough) starting from insensitizing controls in L 2.Ministerio de Educación y CienciaTaylor & FrancisEcuaciones Diferenciales y Análisis NuméricoMinisterio de Educación y Ciencia (MEC). España2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41481https://doi.org/10.1081/PDE-200033749reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésCommunications in Partial Differential Equations, 29 (7-8), 1017-1050.PB98–1134info:eu-repo/semantics/openAccessoai:idus.us.es:11441/414812026-06-17T12:51:07Z
dc.title.none.fl_str_mv Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
title Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
spellingShingle Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
Bodart, Olivier
title_short Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
title_full Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
title_fullStr Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
title_full_unstemmed Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
title_sort Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity
dc.creator.none.fl_str_mv Bodart, Olivier
González Burgos, Manuel
Pérez García, Rosario
author Bodart, Olivier
author_facet Bodart, Olivier
González Burgos, Manuel
Pérez García, Rosario
author_role author
author2 González Burgos, Manuel
Pérez García, Rosario
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
Ministerio de Educación y Ciencia (MEC). España
description In this paper we consider a semilinear heat equation (in a bounded domain Ω of IRN ) with a nonlinearity that has a superlinear growth at infinity. We prove the existence of a control, with support in an open set ω ⊂ Ω, that insensitizes the L2−norm of the observation of the solution in another open subset O ⊂ Ω when ω ∩ O 6= ∅, under suitable assumptions on the nonlinear term f(y) and the right hand side term ξ of the equation. The proof, involving global Carleman estimates and regularizing properties of the heat equation, relies on the sharp study of a similar linearized problem and an appropriate fixed-point argument. For certain superlinear nonlinearities, we also prove an insensitivity result of a negative nature. The crucial point in this paper is the technique of construction of L r–controls (r large enough) starting from insensitizing controls in L 2.
publishDate 2004
dc.date.none.fl_str_mv 2004
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/41481
https://doi.org/10.1081/PDE-200033749
url http://hdl.handle.net/11441/41481
https://doi.org/10.1081/PDE-200033749
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Communications in Partial Differential Equations, 29 (7-8), 1017-1050.
PB98–1134
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 Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
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
repository.mail.fl_str_mv
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score 15.300719

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