Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term

In this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the...

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Autores: Et-Tahri, Fouad, Barcena Petisco, Jon Asier, Boutaayamou, Idriss, Maniar, Lahcen
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/73738
Acceso en línea:http://hdl.handle.net/10810/73738
Access Level:acceso abierto
Palabra clave:Carleman estimates
Uniform controllability
Transport equation
Singular limits
Cost control
Spectral decomposition
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spelling Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport termEt-Tahri, FouadBarcena Petisco, Jon AsierBoutaayamou, IdrissManiar, LahcenCarleman estimatesUniform controllabilityTransport equationSingular limitsCost controlSpectral decompositionIn this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the control cost decays exponentially when the viscosity vanishes and the control time is sufficiently large. On the other hand, if the range of the control region by the transport flow does not cover that of $\Omega$, we prove that the control cost explodes exponentially for the Neumann boundary conditions case with vanishing viscosity and all control time.J.A.B.P. was supported by the Grant PID2021-126813NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” and by the grant IT1615-22 funded by the Basque Government.EDP Sciences202520252024info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/73738reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoInglésinfo:eu-repo/grantAgreement/MCIU/PID2021-126813NB-I00/https://doi.org/10.1051/cocv/2024042info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/© 2024 The authors. Published by EDP Sciences, SMAI. This is an Open Access article distributed under the terms of the Creative Commons Attribution License.oai:addi.ehu.eus:10810/737382026-06-18T09:23:17Z
dc.title.none.fl_str_mv Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
title Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
spellingShingle Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
Et-Tahri, Fouad
Carleman estimates
Uniform controllability
Transport equation
Singular limits
Cost control
Spectral decomposition
title_short Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
title_full Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
title_fullStr Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
title_full_unstemmed Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
title_sort Asymptotic behavior of null-controllablity cost for parabolic equations with vanishing diffusivity and a transport term
dc.creator.none.fl_str_mv Et-Tahri, Fouad
Barcena Petisco, Jon Asier
Boutaayamou, Idriss
Maniar, Lahcen
author Et-Tahri, Fouad
author_facet Et-Tahri, Fouad
Barcena Petisco, Jon Asier
Boutaayamou, Idriss
Maniar, Lahcen
author_role author
author2 Barcena Petisco, Jon Asier
Boutaayamou, Idriss
Maniar, Lahcen
author2_role author
author
author
dc.subject.none.fl_str_mv Carleman estimates
Uniform controllability
Transport equation
Singular limits
Cost control
Spectral decomposition
topic Carleman estimates
Uniform controllability
Transport equation
Singular limits
Cost control
Spectral decomposition
description In this paper we study the null controllability cost of a transport-diffusion system under Robin boundary conditions with distributed control and in which the transport coefficient is a gradient field. First, we provide some conditions on transport coefficient and boundary potential to show that the control cost decays exponentially when the viscosity vanishes and the control time is sufficiently large. On the other hand, if the range of the control region by the transport flow does not cover that of $\Omega$, we prove that the control cost explodes exponentially for the Neumann boundary conditions case with vanishing viscosity and all control time.
publishDate 2024
dc.date.none.fl_str_mv 2024
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/73738
url http://hdl.handle.net/10810/73738
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MCIU/PID2021-126813NB-I00/
https://doi.org/10.1051/cocv/2024042
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv EDP Sciences
publisher.none.fl_str_mv EDP Sciences
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812455

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