Second order optimality conditions for optimal control of quasilinear parabolic equations
Second order optimality conditions for optimal control of quasilinear parabolic equations
Dokument öffnen (577.9KB)Datum der Veröffentlichung
03.2017Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11836
Inhalt
We discuss an optimal control problem governed by a quasilinear parabolic PDE including mixed boundary conditions and Neumann boundary control, as well as distributed control. Second order necessary and sufficient optimality conditions are derived. The latter leads to a quadratic growth condition without two-norm discrepancy. Furthermore, maximal parabolic regularity of the state equation in Bessel-potential spaces HD−ζ,p with uniform bound on the norm of the solution operator is proved and used to derive stability results with respect to perturbations of the nonlinear differential operator.
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.3934/mcrf.2018001Reihe, Nummer
INS Preprints ; 1705Bonifacius, Lucas; Neitzel, Ira: Second order optimality conditions for optimal control of quasilinear parabolic equations. In: INS Preprints, 1705.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11836
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11836
@unpublished{handle:20.500.11811/11836,
author = {{Lucas Bonifacius} and {Ira Neitzel}},
title = {Second order optimality conditions for optimal control of quasilinear parabolic equations},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = mar,
INS Preprints},
volume = 1705,
note = {We discuss an optimal control problem governed by a quasilinear parabolic PDE including mixed boundary conditions and Neumann boundary control, as well as distributed control. Second order necessary and sufficient optimality conditions are derived. The latter leads to a quadratic growth condition without two-norm discrepancy. Furthermore, maximal parabolic regularity of the state equation in Bessel-potential spaces HD−ζ,p with uniform bound on the norm of the solution operator is proved and used to derive stability results with respect to perturbations of the nonlinear differential operator.},
url = {https://hdl.handle.net/20.500.11811/11836}
}
author = {{Lucas Bonifacius} and {Ira Neitzel}},
title = {Second order optimality conditions for optimal control of quasilinear parabolic equations},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = mar,
INS Preprints},
volume = 1705,
note = {We discuss an optimal control problem governed by a quasilinear parabolic PDE including mixed boundary conditions and Neumann boundary control, as well as distributed control. Second order necessary and sufficient optimality conditions are derived. The latter leads to a quadratic growth condition without two-norm discrepancy. Furthermore, maximal parabolic regularity of the state equation in Bessel-potential spaces HD−ζ,p with uniform bound on the norm of the solution operator is proved and used to derive stability results with respect to perturbations of the nonlinear differential operator.},
url = {https://hdl.handle.net/20.500.11811/11836}
}
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