Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 2, pp. 469 - 489 (1999)
Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
K. Malanowski and F. TröltzschK. Malanowski: Polish Acad. Sci., Systems Res. Inst., ul. Newelska 6, P--01-447 Warszawa
F. Tröltzsch: Techn. Univ. Chemnitz-Zwickau, Fak. Math., D--09107 Chemnitz
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 $L^\infty$-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong.
Keywords: parametric optimal control, semilinear parabolic equations, Lipschitz stability, generalized equations
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