Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

Submission Status:epub ahead of print
  • We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.

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Metadaten
Author:Günter Leugering
DOI:https://doi.org/https://doi.org/10.4236/am.2017.88082
ISSN:2152-7393
Document Type:Periodical
Language:English
Date of Publication (online):2017/08/17
Date of first Publication:2017/10/12
Release Date:2017/10/12
Tag:nonoverlapping omain decomposition, optimal control of semi-linear ellioptic systems on netowrks
GND Keyword:28
Volume:8
Page Number:1074-1099
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:A05