Optimizing the fractional power in a model with stochastic PDE constraints

Carina Geldhauser; Enrico Valdinoci

doi:10.1515/ans-2018-2031

Optimizing the fractional power in a model with stochastic PDE constraints

Carina Geldhauser, Enrico Valdinoci

School of Physics, Mathematics and Computing

Research output: Contribution to journal › Article

2 Citations (Scopus)

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
Pages (from-to)	649-669
Number of pages	21
Journal	Advanced Nonlinear Studies
Volume	18
Issue number	4
DOIs	https://doi.org/10.1515/ans-2018-2031
Publication status	Published - 1 Nov 2018

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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.",

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N2 - 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.

AB - 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.

KW - Fractional Parameter

KW - Optimal Control

KW - Optimization

KW - Stochastic Heat Equation

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