Abstract
We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation. Well-posedness of the state equation and differentiability properties with respect to the fractional parameter s are established. We show that under certain conditions on the noise, optimality conditions for the control problem can be established.
Original language | English |
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Pages (from-to) | 649-669 |
Number of pages | 21 |
Journal | Advanced Nonlinear Studies |
Volume | 18 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Nov 2018 |