Identification of the friction function in a semilinear system for gas transport through a network. (3rd May 2020)

• Record Type: Journal Article
• Authors: Hintermüller, Michael; Strogies, Nikolai
• Is Part Of: Optimization methods and software. Volume 35:Number 3(2020)
• Page Start: 576
• Page End: 617
• Publication Date: 2020-05-03
• Subjects: Inverse problem -- output-least squares problem -- uncertainty quantification -- balance law -- gas networks; 34K28 -- 49J30 -- 34K29 -- 49M05 -- 76N15; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2019.1692206
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: An identification problem for the friction parameter in a semilinear system of balance laws, describing the transport of gas through a passive network of pipelines, is considered. The existence of broad solutions to the state system is proven and sensitivity results for the corresponding solution operator are obtained. The existence of solutions to the output least squares formulation of the identification problem, based on noisy measurements over time at fixed spatial positions, is established. Finally, numerical experiments validate the theoretical findings.