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

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Abstract

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 metrisable control sets.
Original languageEnglish
Pages (from-to)2664–2703
JournalSIAM J. Control Optim.
Volume51
Issue number3
Publication statusPublished - Mar 2010

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