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  <doc>
    <id>415</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>18</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-08-20</completedDate>
    <publishedDate>2021-08-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Space-Time-Domain Decomposition for Optimal Control Problems Governed by Linear Hyperbolic Systems</title>
    <abstract language="eng">In this article, we combine a domain decomposition method in space and time for optimal control problems with PDE-constraints described by Lagnese and Leugering to a simultaneous space-time decomposition applied to optimal control problems for systems of linear hyperbolic equations with distributed control. We thereby extend the recent work by Krug et al. and answer a long standing open question as to whether the combination of time- and space domain decomposition for the method under consideration can be put into one single convergent iteration procedure. The algorithm is designed for a semi-elliptic system of equations obtained from the hyperbolic optimality system by the way of reduction to the adjoint state. The focus is on the relation to the classical procedure introduced by Lions for elliptic problems.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">false</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Günter Leugering</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Space- and time-domain decomposition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear hyperbolic systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Convergence</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>A posteriori error estimates</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/415/space-time-domain-decompostion.pdf</file>
  </doc>
</export-example>
