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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Bibliographic Details
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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Summary: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.

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