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 › peer-review

7 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

Access to Document

10.1515/ans-2018-2031

Cite this

@article{1af4bb398efb4775b12d0ada908d7588,

title = "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 = "Fractional Parameter, Optimal Control, Optimization, Stochastic Heat Equation",

author = "Carina Geldhauser and Enrico Valdinoci",

year = "2018",

month = nov,

day = "1",

doi = "10.1515/ans-2018-2031",

language = "English",

volume = "18",

pages = "649--669",

journal = "Advanced Nonlinear Studies",

issn = "1536-1365",

publisher = "De Gruyter Mouton",

number = "4",

}

TY - JOUR

T1 - Optimizing the fractional power in a model with stochastic PDE constraints

AU - Geldhauser, Carina

AU - Valdinoci, Enrico

PY - 2018/11/1

Y1 - 2018/11/1

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

UR - http://www.scopus.com/inward/record.url?scp=85053700583&partnerID=8YFLogxK

U2 - 10.1515/ans-2018-2031

DO - 10.1515/ans-2018-2031

M3 - Article

AN - SCOPUS:85053700583

VL - 18

SP - 649

EP - 669

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

SN - 1536-1365

IS - 4

ER -

Optimizing the fractional power in a model with stochastic PDE constraints

Abstract

Access to Document

Other files and links

Fingerprint

Cite this