Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces
Título de la revista
Serrano Perdomo, Rafael Antonio
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.
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