Optimizing the Fractional Power in a Model with Stochastic PDE Constraints-Reference-Cited by-同舟云学术

Optimizing the Fractional Power in a Model with Stochastic PDE Constraints

Published:2018-09-13 Issue:4 Volume:18 Page:649-669
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Geldhauser Carina¹^ORCID,Valdinoci Enrico²^ORCID

Affiliation:

1. Chebyshev Laboratory , St. Petersburg State University , 14th Line V.O., 29B , Saint Petersburg 199178 Russia

2. Department of Mathematics and Statistics , University of Western Australia , 35 Stirling Highway, Crawley , Perth , Western Australia 6009 , Australia ; and Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milan; and Istituto di Matematica Applicata e Tecnologie Informatiche, Consiglio Nazionale delle Ricerche, Via Ferrata 1, 27100 Pavia, Italy

Abstract

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.

Funder

Russian Science Foundation

Australian Research Council

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2018-2031/pdf

Reference27 articles.

1. N. Abatangelo and E. Valdinoci, Getting Acquainted with the Fractional Laplacian, Springer INdAM Ser., Springer, Cham, 2019.

2. H. Antil and E. Otárola, A FEM for an optimal control problem of fractional powers of elliptic operators, SIAM J. Control Optim. 53 (2015), no. 6, 3432–3456. 10.1137/140975061