Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces

We study an optimal relaxed control problem for a class of semilinear stochastic PDEs on Banach spaces perturbed by multiplicative noise and driven by a cylindrical Wiener process. The state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative-type...

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Tipo de recurso:
Fecha de publicación:
2013
Institución:
Universidad del Rosario
Repositorio:
Repositorio EdocUR - U. Rosario
Idioma:
eng
OAI Identifier:
oai:repository.urosario.edu.co:10336/23298
Acceso en línea:
https://doi.org/10.1137/100788574
https://repository.urosario.edu.co/handle/10336/23298
Palabra clave:
Control set
Multiplicative cylindrical noise
Relaxed control
Stochastic PDE
Young measure
Convolution
Equations of state
Factorization
Nonlinear equations
Optimization
Stochastic systems
Banach spaces
Multiplicative cylindrical noise
Relaxed control
Stochastic convolution
Stochastic PDE
Suslin control set
UMD type-2 Banach spaces
Young measures
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network_acronym_str EDOCUR2
network_name_str Repositorio EdocUR - U. Rosario
repository_id_str
spelling 53a0fbd8-f0f4-4b98-b41a-81abc374c34e800853686002020-05-26T00:01:00Z2020-05-26T00:01:00Z2013We study an optimal relaxed control problem for a class of semilinear stochastic PDEs on Banach spaces perturbed by multiplicative noise and driven by a cylindrical Wiener process. The state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative-type condition with respect to the state variable. The main tools of our study are the factorization method for stochastic convolutions in UMD type-2 Banach spaces and certain compactness properties of the factorization operator and of the class of Young measures on Suslin metrizable control sets. © 2013 Society for Industrial and Applied Mathematics.application/pdfhttps://doi.org/10.1137/1007885741095713803630129https://repository.urosario.edu.co/handle/10336/23298eng2703No. 32664SIAM Journal on Control and OptimizationVol. 51SIAM Journal on Control and Optimization, ISSN:10957138, 03630129, Vol.51, No.3 (2013); pp. 2664-2703https://www.scopus.com/inward/record.uri?eid=2-s2.0-84884852919&doi=10.1137%2f100788574&partnerID=40&md5=cd5c40e888c4d097679b6c8ab3d8904aAbierto (Texto Completo)http://purl.org/coar/access_right/c_abf2instname:Universidad del Rosarioreponame:Repositorio Institucional EdocURControl setMultiplicative cylindrical noiseRelaxed controlStochastic PDEYoung measureConvolutionEquations of stateFactorizationNonlinear equationsOptimizationStochastic systemsBanach spacesMultiplicative cylindrical noiseRelaxed controlStochastic convolutionStochastic PDESuslin control setUMD type-2 Banach spacesYoung measuresOptimal relaxed control of dissipative stochastic partial differential equations in Banach spacesarticleArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501Brze?niak Z.Serrano Perdomo, Rafael Antonio10336/23298oai:repository.urosario.edu.co:10336/232982021-10-25 20:59:43.072https://repository.urosario.edu.coRepositorio institucional EdocURedocur@urosario.edu.co
dc.title.spa.fl_str_mv Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
title Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
spellingShingle Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
Control set
Multiplicative cylindrical noise
Relaxed control
Stochastic PDE
Young measure
Convolution
Equations of state
Factorization
Nonlinear equations
Optimization
Stochastic systems
Banach spaces
Multiplicative cylindrical noise
Relaxed control
Stochastic convolution
Stochastic PDE
Suslin control set
UMD type-2 Banach spaces
Young measures
title_short Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
title_full Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
title_fullStr Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
title_full_unstemmed Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
title_sort Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
dc.subject.keyword.spa.fl_str_mv Control set
Multiplicative cylindrical noise
Relaxed control
Stochastic PDE
Young measure
Convolution
Equations of state
Factorization
Nonlinear equations
Optimization
Stochastic systems
Banach spaces
Multiplicative cylindrical noise
Relaxed control
Stochastic convolution
Stochastic PDE
Suslin control set
UMD type-2 Banach spaces
Young measures
topic Control set
Multiplicative cylindrical noise
Relaxed control
Stochastic PDE
Young measure
Convolution
Equations of state
Factorization
Nonlinear equations
Optimization
Stochastic systems
Banach spaces
Multiplicative cylindrical noise
Relaxed control
Stochastic convolution
Stochastic PDE
Suslin control set
UMD type-2 Banach spaces
Young measures
description We study an optimal relaxed control problem for a class of semilinear stochastic PDEs on Banach spaces perturbed by multiplicative noise and driven by a cylindrical Wiener process. The state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative-type condition with respect to the state variable. The main tools of our study are the factorization method for stochastic convolutions in UMD type-2 Banach spaces and certain compactness properties of the factorization operator and of the class of Young measures on Suslin metrizable control sets. © 2013 Society for Industrial and Applied Mathematics.
publishDate 2013
dc.date.created.spa.fl_str_mv 2013
dc.date.accessioned.none.fl_str_mv 2020-05-26T00:01:00Z
dc.date.available.none.fl_str_mv 2020-05-26T00:01:00Z
dc.type.eng.fl_str_mv article
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.spa.spa.fl_str_mv Artículo
dc.identifier.doi.none.fl_str_mv https://doi.org/10.1137/100788574
dc.identifier.issn.none.fl_str_mv 10957138
03630129
dc.identifier.uri.none.fl_str_mv https://repository.urosario.edu.co/handle/10336/23298
url https://doi.org/10.1137/100788574
https://repository.urosario.edu.co/handle/10336/23298
identifier_str_mv 10957138
03630129
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.citationEndPage.none.fl_str_mv 2703
dc.relation.citationIssue.none.fl_str_mv No. 3
dc.relation.citationStartPage.none.fl_str_mv 2664
dc.relation.citationTitle.none.fl_str_mv SIAM Journal on Control and Optimization
dc.relation.citationVolume.none.fl_str_mv Vol. 51
dc.relation.ispartof.spa.fl_str_mv SIAM Journal on Control and Optimization, ISSN:10957138, 03630129, Vol.51, No.3 (2013); pp. 2664-2703
dc.relation.uri.spa.fl_str_mv https://www.scopus.com/inward/record.uri?eid=2-s2.0-84884852919&doi=10.1137%2f100788574&partnerID=40&md5=cd5c40e888c4d097679b6c8ab3d8904a
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.acceso.spa.fl_str_mv Abierto (Texto Completo)
rights_invalid_str_mv Abierto (Texto Completo)
http://purl.org/coar/access_right/c_abf2
dc.format.mimetype.none.fl_str_mv application/pdf
institution Universidad del Rosario
dc.source.instname.spa.fl_str_mv instname:Universidad del Rosario
dc.source.reponame.spa.fl_str_mv reponame:Repositorio Institucional EdocUR
repository.name.fl_str_mv Repositorio institucional EdocUR
repository.mail.fl_str_mv edocur@urosario.edu.co
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