A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions

In this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form ∂ny + f(y)=0 are considered. The problem leads to an analysis of a special type of nonlinear null controllability problem. A sharp study of...

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Detalles Bibliográficos
Autores: Bodart, Olivier, González Burgos, Manuel, Pérez García, Rosario
Tipo de recurso: artículo
Estado:Versión publicada
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:11441/41470
Acceso en línea:http://hdl.handle.net/11441/41470
https://doi.org/10.1137/S036301290343161X
Access Level:acceso abierto
Palabra clave:controllability
nonlinear PDE of parabolic type
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spelling A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditionsBodart, OlivierGonzález Burgos, ManuelPérez García, Rosariocontrollabilitynonlinear PDE of parabolic typeIn this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form ∂ny + f(y)=0 are considered. The problem leads to an analysis of a special type of nonlinear null controllability problem. A sharp study of the linear case and a later application of an appropriate fixed point argument constitute the scheme of the proof of the main result. The boundary conditions we are dealing with lead us to seek a fixed point, and thus also control functions, in certain H¨older spaces. The main strategy in this paper is the construction of controls with H¨olderian regularity starting from L2-controls in the linear case. Sufficient regularity in the data and appropriate assumptions on the right-hand side term ξ of the equation are required.Ministerio de Educación y CienciaSociety for Industrial and Applied MathematicsEcuaciones Diferenciales y Análisis NuméricoMinisterio de Educación y Ciencia (MEC). España2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41470https://doi.org/10.1137/S036301290343161Xreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésSIAM Journal on Control and Optimization, 43 (3), 955-969.PB98–1134http://dx.doi.org/10.1137/S036301290343161Xinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/414702026-06-17T12:51:07Z
dc.title.none.fl_str_mv A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
title A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
spellingShingle A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
Bodart, Olivier
controllability
nonlinear PDE of parabolic type
title_short A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
title_full A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
title_fullStr A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
title_full_unstemmed A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
title_sort A local result on insensitizing controls for a semilinear heat equation with nonlinear boundary Fourier conditions
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
dc.subject.none.fl_str_mv controllability
nonlinear PDE of parabolic type
topic controllability
nonlinear PDE of parabolic type
description In this paper we present a local result on the existence of insensitizing controls for a semilinear heat equation when nonlinear boundary conditions of the form ∂ny + f(y)=0 are considered. The problem leads to an analysis of a special type of nonlinear null controllability problem. A sharp study of the linear case and a later application of an appropriate fixed point argument constitute the scheme of the proof of the main result. The boundary conditions we are dealing with lead us to seek a fixed point, and thus also control functions, in certain H¨older spaces. The main strategy in this paper is the construction of controls with H¨olderian regularity starting from L2-controls in the linear case. Sufficient regularity in the data and appropriate assumptions on the right-hand side term ξ of the equation are required.
publishDate 2004
dc.date.none.fl_str_mv 2004
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/11441/41470
https://doi.org/10.1137/S036301290343161X
url http://hdl.handle.net/11441/41470
https://doi.org/10.1137/S036301290343161X
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv SIAM Journal on Control and Optimization, 43 (3), 955-969.
PB98–1134
http://dx.doi.org/10.1137/S036301290343161X
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
repository.mail.fl_str_mv
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