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 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.

• 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
• License: Abierto (Texto Completo)