Casas, E., Dominguez Corella, A., & Jork, N. A. (2023). New Assumptions for Stability Analysis in Elliptic Optimal Control Problems. SIAM Journal on Control and Optimization, 61(3), 1394–1414. https://doi.org/10.1137/22M149199X
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 may not even appear explicitly in the objective functional. Under new assumptions, we prove Lipschitz stability of the optimal controls and associated states with respect to not only perturbations in the equation and the objective functional but also the Tikhonov regularization parameter.
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Project title:
Regularität von Abbildungen - Theorie und Anwendungen: I 4571-N (FWF 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%
