Casas Eduardo, Dominguez Corella, A., & Jork, N. A. (2022). New assumptions for stability analysis in elliptic optimal control problems (No. 2022–02). https://doi.org/10.34726/3064
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Series:
Research Reports
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Report No.:
2022-02
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Date (published):
May-2022
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Number of Pages:
21
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Keywords:
control problems; semilinear elliptic equations; Tikhonov regularization
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Abstract:
This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the presence of a convection term. The control appears only linearly, or even it can not appear in a explicit form in the objective functional. Under new assumptions, we prove Lipschitz stability of the optimal controls and associated states with respect to perturbations in the equation and the objective functional as well as with respect to the Tikhonov regularization parameter.
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Project title:
Regularität von Abbildungen - Theorie und Anwendungen: I 4571-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Project (external):
MCIN/ AEI/10.13039/501100011033
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Project ID:
PID2020-114837GB-I00
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Research Areas:
Mathematical and Algorithmic Foundations: 20% Fundamental Mathematics Research: 80%
