Exact controllability to the trajectories of the one-phase Stefan problem

This paper deals with the boundary exact controllability to the trajectories of the one-phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. We prove the local exact controllability to (smooth) trajectories. To this purpose,...

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Detalhes bibliográficos
Autores: Bárcena Petisco, Jon Asier, Fernández Cara, Enrique, Araujo de Souza, Diego
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2023
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/154255
Acesso em linha:https://hdl.handle.net/11441/154255
https://doi.org/10.1016/j.jde.2023.08.016
Access Level:acceso abierto
Palavra-chave:Free-boundary problems
One-phase Stefan problem
Exact controllability to the trajectories
Global Carleman inequalities
Inverse function theorem
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spelling Exact controllability to the trajectories of the one-phase Stefan problemBárcena Petisco, Jon AsierFernández Cara, EnriqueAraujo de Souza, DiegoFree-boundary problemsOne-phase Stefan problemExact controllability to the trajectoriesGlobal Carleman inequalitiesInverse function theoremThis paper deals with the boundary exact controllability to the trajectories of the one-phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. We prove the local exact controllability to (smooth) trajectories. To this purpose, we first reformulate the problem as the local null controllability of a coupled PDE-ODE system with distributed controls. Then, a new Carleman inequality for the adjoint of the linearized PDE-ODE system, coupled on the boundary through nonlocal in space and memory terms, is presented. This leads to the null controllability of an appropriate linear system. Finally, the result is obtained via local inversion, by using Lyusternik-Graves' Theorem. As a byproduct of our approach, we find that some parabolic equations which contains memory terms located on the boundary are null-controllable.ElsevierEcuaciones Diferenciales y Análisis NuméricoFQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/154255https://doi.org/10.1016/j.jde.2023.08.016reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Differential Equations, 376, 126-153.https://doi.org/10.1016/j.jde.2023.08.016info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1542552026-06-17T12:51:07Z
dc.title.none.fl_str_mv Exact controllability to the trajectories of the one-phase Stefan problem
title Exact controllability to the trajectories of the one-phase Stefan problem
spellingShingle Exact controllability to the trajectories of the one-phase Stefan problem
Bárcena Petisco, Jon Asier
Free-boundary problems
One-phase Stefan problem
Exact controllability to the trajectories
Global Carleman inequalities
Inverse function theorem
title_short Exact controllability to the trajectories of the one-phase Stefan problem
title_full Exact controllability to the trajectories of the one-phase Stefan problem
title_fullStr Exact controllability to the trajectories of the one-phase Stefan problem
title_full_unstemmed Exact controllability to the trajectories of the one-phase Stefan problem
title_sort Exact controllability to the trajectories of the one-phase Stefan problem
dc.creator.none.fl_str_mv Bárcena Petisco, Jon Asier
Fernández Cara, Enrique
Araujo de Souza, Diego
author Bárcena Petisco, Jon Asier
author_facet Bárcena Petisco, Jon Asier
Fernández Cara, Enrique
Araujo de Souza, Diego
author_role author
author2 Fernández Cara, Enrique
Araujo de Souza, Diego
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software
dc.subject.none.fl_str_mv Free-boundary problems
One-phase Stefan problem
Exact controllability to the trajectories
Global Carleman inequalities
Inverse function theorem
topic Free-boundary problems
One-phase Stefan problem
Exact controllability to the trajectories
Global Carleman inequalities
Inverse function theorem
description This paper deals with the boundary exact controllability to the trajectories of the one-phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. We prove the local exact controllability to (smooth) trajectories. To this purpose, we first reformulate the problem as the local null controllability of a coupled PDE-ODE system with distributed controls. Then, a new Carleman inequality for the adjoint of the linearized PDE-ODE system, coupled on the boundary through nonlocal in space and memory terms, is presented. This leads to the null controllability of an appropriate linear system. Finally, the result is obtained via local inversion, by using Lyusternik-Graves' Theorem. As a byproduct of our approach, we find that some parabolic equations which contains memory terms located on the boundary are null-controllable.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/154255
https://doi.org/10.1016/j.jde.2023.08.016
url https://hdl.handle.net/11441/154255
https://doi.org/10.1016/j.jde.2023.08.016
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Differential Equations, 376, 126-153.
https://doi.org/10.1016/j.jde.2023.08.016
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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