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Malanowski, Kazimierz [Author]; Tröltzsch, Fredi [Author]

Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations

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  • Media type: Preprint
  • Title: Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
  • Contributor: Malanowski, Kazimierz [Author]; Tröltzsch, Fredi [Author]
  • imprint: Chemnitz: Technische Universität Chemnitz, [1998]
  • Language: English
  • Keywords: MSC 49K40 ; semilinear parabolic equations ; optimal control ; supremum norm ; Lipschitz stability ; MSC 49K20
  • Origination:
  • Footnote:
  • Description: A class of parametric optimal control problems for semilinear parabolicequations is considered. Using recent regularity results for solutions of such equations,sufficient conditions are derived under which the solutions to optimal control problemsare locally Lipschitz continuous functions of the parameter in the L1-norm. It is shownthat these conditions are also necessary, provided that the dependence of data on theparameter is sufficiently strong.