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  <doc>
    <id>318</id>
    <completedYear>2020</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2020-07-29</completedDate>
    <publishedDate>2020-07-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Closed loop control of gas flow in a pipe: Stability for a transient model</title>
    <abstract language="eng">This contribution focuses on the analysis and control of friction-dominated flow of gas in pipes. The pressure in the gas flow is governed by a partial differential equation that is a doubly nonlinear parabolic equation of p-Laplace type, where p=2/3. Such equations exhibit positive solutions, finite speed of propagation and satisfy a maximum principle. The pressure is fixed on one end (upstream), and the flow is specified on the other end (downstream). These boundary conditions determine a unique steady equilibrium flow. We present a boundary feedback flow control scheme, that ensures local exponential stability of the equilibrium in an L2-sense. The analysis is done both for the pde system and an ode system that is obtained by a suitable spatial semi-discretization. The proofs are based upon suitably chosen Lyapunov functions.</abstract>
    <parentTitle language="deu">at - Automatisierungstechnik</parentTitle>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Martin Gugat</author>
    <author>Falk Hante</author>
    <author>Li Jin</author>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="institutes" number="">Humboldt-Universität zu Berlin</collection>
    <collection role="subprojects" number="">A03</collection>
    <collection role="subprojects" number="">C03</collection>
    <collection role="subprojects" number="">Z01</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/318/Manuscript.pdf</file>
  </doc>
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