Optimizing the Fractional Power in a Model with Stochastic PDE Constraints

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.

Keywords

• stochastic heat equation
• optimization
• optimal control
• fractional parameter
• 65k10
• 35r60
• 35r11