<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>482</id>
    <completedYear>2022</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>15</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2022-01-12</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Nonoverlapping Domain Decomposition for Instantaneous Optimal Control of Friction Dominated Flow in a Gas-Network</title>
    <abstract language="eng">We consider a non-overlapping domain decomposition method for an optimal control problem related to the flow of gas in a pipe network. The equations of motions are taken to be represented by a friction dominated model derived from a semi-linear approximation of the fully nonlinear isothermal Euler gas equations. This involves a p-Laplace-type problem on the graph with p = 3/2. We continue the work by Leugering and Mophou where such a problem has been discussed in the context of an instantaneous control strategy. We provide a non-overlapping domain decomposition in the spirit of P.L. Lions for elliptic problems and extend the method to the first order optimality system.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Günter Leugering</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gas networks</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>p-Laplace problem on a graph</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimality system</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Domain decomposition</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="subprojects" number="">A05</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/482/Leugering_TRR154_31_01_22.pdf</file>
  </doc>
</export-example>
