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@PHDTHESIS{OConnor:752383,
      author       = {O'Connor, Robert Gerard},
      othercontributors = {Grepl, Martin Alexander and Stamm, Benjamin and Volkwein,
                          Stefan},
      title        = {{R}educed basis methods for the analysis, simulation, and
                      control of noncoercive parabolic systems},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2018-232017},
      pages        = {1 Online-Ressource (xi, 168 Seiten) : Illustrationen},
      year         = {2018},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2018},
      abstract     = {In this thesis we present new methods for the analysis,
                      simulation, and control of parameter-dependent parabolic
                      problems. These methods are all closely related to the
                      reduced basis method and greatly reduce the computational
                      cost of solving various types of problems for a large number
                      of parameter values. The main advantage of our methods is
                      that they can handle systems with non coercive operators.
                      Previous reduced basis methods for the optimal control of
                      parabolic systems were only valid for coercive systems. We
                      present the first method that can also handle non coercive
                      problems. That is done by extending space-time methods that
                      were proposed for the simulation of parabolic problems. We
                      also introduce the use of Lyapunov's stability theory in
                      reduced basis modeling. This opens many new possibilities in
                      the area of control and systems theory. To make such
                      applications possible we present an extension of the
                      successive constraint method to linear matrix inequalities.
                      Such inequalities play an essential role in many
                      applications involving Lyapunov stability. The first method
                      that we present allows for many new applications but is
                      limited in that the decision variable needs to be low
                      dimensional. We then show how that method can be extended
                      and used in constructing Lyapunov functions for non coercive
                      systems.As a final application we demonstrate how Lyapunov
                      functions can be used to derive reduced basis error bounds
                      for non coercive parabolic systems. Such error bounds are
                      often more cost efficient than space-time bounds and benefit
                      from a more accurate understanding of the system's
                      underlying dynamics.},
      cin          = {111410 / 110000},
      ddc          = {510},
      cid          = {$I:(DE-82)111410_20140620$ / $I:(DE-82)110000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2018-232017},
      url          = {https://publications.rwth-aachen.de/record/752383},
}