<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>388</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-05-18</completedDate>
    <publishedDate>2021-05-18</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Constrained exact boundary controllability of a semilinear model for pipeline gas flow</title>
    <abstract language="eng">While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures. We prove an existence result for continuous solutions of the semilinear model that takes into account lower and upper bounds for the pressure and an upper bound for the magnitude of the Mach number of the gas flow. These state constraints are important both in the operation of gas pipelines and to guarantee that the solution remains in the set where the model is physically valid. We show the constrained exact boundary controllability of the system with the same pressure and Mach number constraints.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Martin Gugat</author>
    <author>Jens Habermann</author>
    <author>Michael Hintermüller</author>
    <author>Olivier Huber</author>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="institutes" number="">Humboldt-Universität zu Berlin</collection>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">B02</collection>
    <collection role="subprojects" number="">C03</collection>
    <collection role="subprojects" number="">C05</collection>
    <collection role="subprojects" number="">C07</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/388/constrained-exact-boundary-control-semilinear.pdf</file>
  </doc>
</export-example>
