Malanowski, Kazimierz; Tröltzsch, Fredi : Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations

Author(s) :

Malanowski, Kazimierz; Tröltzsch, Fredi

Title :

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

Electronic source :

[gzipped ps-file] 75 kB

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-15, 1998

Mathematics Subject Classification :

49K20 [ Optimal control problems with PDE (nec./ suff.) ]

49K40 [ Sensitivity of optimal solutions in the presence of perturbations ]

Abstract :

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.

Keywords :

optimal control, semilinear parabolic equations, Lipschitz stability, supremum norm

Language :

english

Publication time :

7/1998

Notes :

Dedicated to the 65. birthday of Prof. Lothar von Wolfersdorf