Null controllability of viscous Hamilton-Jacobi equations

We study the problem of null controllability for viscous Hamilton-Jacobi equations in bounded domains of the Euclidean space in any space dimension and with controls localized in an arbitrary open nonempty subset of the domain where the equation holds. We prove the null controllability of the system...

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Detalles Bibliográficos
Autores: Porretta, A., Zuazua, E.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/564
Acceso en línea:http://hdl.handle.net/20.500.11824/564
Access Level:acceso abierto
Palabra clave:Decay estimates
Null controllability
Viscous Hamilton-Jacobi equations
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spelling Null controllability of viscous Hamilton-Jacobi equationsPorretta, A.Zuazua, E.Decay estimatesNull controllabilityViscous Hamilton-Jacobi equationsWe study the problem of null controllability for viscous Hamilton-Jacobi equations in bounded domains of the Euclidean space in any space dimension and with controls localized in an arbitrary open nonempty subset of the domain where the equation holds. We prove the null controllability of the system in the sense that, every bounded (and in some cases uniformly continuous) initial datum can be driven to the null state in a sufficiently large time. The proof combines decay properties of the solutions of the uncontrolled system and local null controllability results for small data obtained by means of Carleman inequalities. We also show that there exists a waiting time so that the time of control needs to be large enough, as a function of the norm of the initial data, for the controllability property to hold. We give sharp asymptotic lower and upper bounds on this waiting time both as the size of the data tends to zero and infinity. These results also establish a limit on the growth of nonlinearities that can be controlled uniformly on a time independent of the initial data.201720172012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/564reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.scopus.com/inward/record.uri?eid=2-s2.0-84861822464&doi=10.1016%2fj.anihpc.2011.11.002&partnerID=40&md5=43af03befbb81eaf6e895c6aad6f9206Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/5642026-06-19T12:47:47Z
dc.title.none.fl_str_mv Null controllability of viscous Hamilton-Jacobi equations
title Null controllability of viscous Hamilton-Jacobi equations
spellingShingle Null controllability of viscous Hamilton-Jacobi equations
Porretta, A.
Decay estimates
Null controllability
Viscous Hamilton-Jacobi equations
title_short Null controllability of viscous Hamilton-Jacobi equations
title_full Null controllability of viscous Hamilton-Jacobi equations
title_fullStr Null controllability of viscous Hamilton-Jacobi equations
title_full_unstemmed Null controllability of viscous Hamilton-Jacobi equations
title_sort Null controllability of viscous Hamilton-Jacobi equations
dc.creator.none.fl_str_mv Porretta, A.
Zuazua, E.
author Porretta, A.
author_facet Porretta, A.
Zuazua, E.
author_role author
author2 Zuazua, E.
author2_role author
dc.subject.none.fl_str_mv Decay estimates
Null controllability
Viscous Hamilton-Jacobi equations
topic Decay estimates
Null controllability
Viscous Hamilton-Jacobi equations
description We study the problem of null controllability for viscous Hamilton-Jacobi equations in bounded domains of the Euclidean space in any space dimension and with controls localized in an arbitrary open nonempty subset of the domain where the equation holds. We prove the null controllability of the system in the sense that, every bounded (and in some cases uniformly continuous) initial datum can be driven to the null state in a sufficiently large time. The proof combines decay properties of the solutions of the uncontrolled system and local null controllability results for small data obtained by means of Carleman inequalities. We also show that there exists a waiting time so that the time of control needs to be large enough, as a function of the norm of the initial data, for the controllability property to hold. We give sharp asymptotic lower and upper bounds on this waiting time both as the size of the data tends to zero and infinity. These results also establish a limit on the growth of nonlinearities that can be controlled uniformly on a time independent of the initial data.
publishDate 2012
dc.date.none.fl_str_mv 2012
2017
2017
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dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/564
url http://hdl.handle.net/20.500.11824/564
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.scopus.com/inward/record.uri?eid=2-s2.0-84861822464&doi=10.1016%2fj.anihpc.2011.11.002&partnerID=40&md5=43af03befbb81eaf6e895c6aad6f9206
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
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