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  <doc>
    <id>1474</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2012-02-24</completedDate>
    <publishedDate>2012-02-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An optimal control problem in polyconvex hyperelasticity</title>
    <abstract language="eng">We consider a shape implant design problem that arises in the context of facial surgery. &#13;
We introduce a reformulation as an optimal control problem, where the control acts&#13;
as a boundary force. The state is modelled as a minimizer of a polyconvex&#13;
hyperelastic energy functional. We show existence of optimal solutions and&#13;
derive - on a formal level - first order optimality conditions. Finally, preliminary numerical results &#13;
are presented.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="serial">12-08</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-14745</identifier>
    <submitter>Lars Lubkoll</submitter>
    <author>Lars Lubkoll</author>
    <author>Anton Schiela</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>12-08</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyconvex elasticity</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>implant design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <collection role="msc" number="49J20">Optimal control problems involving partial differential equations</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="74B20">Nonlinear elasticity</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="FacialSurgery">FacialSurgery</collection>
    <collection role="projects" number="MATHEON-A17">MATHEON-A17</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1474/ZR-12-08.pdf</file>
  </doc>
</export-example>
