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Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces. (English) Zbl 1283.60092
The authors consider controlled semilinear stochastic evolution equations in Banach spaces, driven by cylindrical Wiener processes. The drift coefficient satisfies a dissipative-type condition with respect to the state variable. To prove the existence of an optimal weak relaxed control, the authors apply a factorization method of stochastic convolutions.
The results are illustrated by examples that cover a class of stochastic reaction-diffusion equations with multiplicative noise.

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
49J20 Existence theories for optimal control problems involving partial differential equations
93E20 Optimal stochastic control
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