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

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

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A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the...

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Main Authors: Malanowski, Kazimierz, Tröltzsch, Fredi
Language:English
Published: Technische Universität Chemnitz 1998
Subjects:
info:eu-repo/classification/ddc/510
ddc:510
optimal control
semilinear parabolic equations
Lipschitz stability
supremum norm
MSC 49K20
MSC 49K40
Online Access:http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801001
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spelling ndltd-DRESDEN-oai-qucosa-de-qucosa-174752021-03-30T05:05:43Z Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations urn:nbn:de:bsz:ch1-199801001 eng A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong. info:eu-repo/classification/ddc/510 ddc:510 optimal control semilinear parabolic equations Lipschitz stability supremum norm MSC 49K20 MSC 49K40 Malanowski, Kazimierz Tröltzsch, Fredi Technische Universität Chemnitz 1998-10-30 info:eu-repo/semantics/openAccess doc-type:preprint info:eu-repo/semantics/preprint doc-type:Text https://monarch.qucosa.de/id/qucosa%3A17475 https://monarch.qucosa.de/api/qucosa%3A17475/attachment/ATT-0/ https://monarch.qucosa.de/api/qucosa%3A17475/attachment/ATT-1/ https://monarch.qucosa.de/api/qucosa%3A17475/attachment/ATT-2/
collection NDLTD
language English
sources NDLTD
topic info:eu-repo/classification/ddc/510
ddc:510
optimal control
semilinear parabolic equations
Lipschitz stability
supremum norm
MSC 49K20
MSC 49K40
spellingShingle info:eu-repo/classification/ddc/510
ddc:510
optimal control
semilinear parabolic equations
Lipschitz stability
supremum norm
MSC 49K20
MSC 49K40
Malanowski, Kazimierz
Tröltzsch, Fredi
Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
description A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong.
author Malanowski, Kazimierz
Tröltzsch, Fredi
author_facet Malanowski, Kazimierz
Tröltzsch, Fredi
author_sort Malanowski, Kazimierz
title Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
title_short Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
title_full Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
title_fullStr Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
title_full_unstemmed Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
title_sort lipschitz stability of solutions to parametric optimal control problems for parabolic equations
publisher Technische Universität Chemnitz
publishDate 1998
url http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801001
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work_keys_str_mv AT malanowskikazimierz lipschitzstabilityofsolutionstoparametricoptimalcontrolproblemsforparabolicequations
AT troltzschfredi lipschitzstabilityofsolutionstoparametricoptimalcontrolproblemsforparabolicequations
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