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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Detalles Bibliográficos
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
Descripción
Sumario: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.