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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Autores Principales: Brze?niak Z., Serrano, Rafael
Formato: Artículo (Article)
Lenguaje:Inglés (English)
Publicado: 2013
Materias:
Acceso en línea:https://repository.urosario.edu.co/handle/10336/23298
https://doi.org/10.1137/100788574
id ir-10336-23298
recordtype dspace
spelling ir-10336-232982021-10-26T01:59:43Z Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces Brze?niak Z. Serrano, Rafael 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 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. 2013 2020-05-26T00:01:00Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 10957138 03630129 https://repository.urosario.edu.co/handle/10336/23298 https://doi.org/10.1137/100788574 eng info:eu-repo/semantics/openAccess application/pdf instname:Universidad del Rosario reponame:Repositorio Institucional EdocUR
institution EdocUR - Universidad del Rosario
collection DSpace
language Inglés (English)
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
spellingShingle 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
Brze?niak Z.
Serrano, Rafael
Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
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.
format Artículo (Article)
author Brze?niak Z.
Serrano, Rafael
author_facet Brze?niak Z.
Serrano, Rafael
author_sort Brze?niak Z.
title Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
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
publishDate 2013
url https://repository.urosario.edu.co/handle/10336/23298
https://doi.org/10.1137/100788574
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score 12,131701