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arXiv · 2212.11046

Second-order optimality conditions for the bilinear optimal control of a degenerate equation

Cyrille Kenne·Landry Djomegne·Pascal Zongo
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Abstract

The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of the state equation, as well as weak maximum principles are established. We prove some differentiability properties of the control-to-state operator and the existence of optimal solutions. Finally, we derive first- and second-order optimality conditions for the system.

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Cyrille Kenne, Landry Djomegne, Pascal Zongo. 2022-12-21. Second-order optimality conditions for the bilinear optimal control of a degenerate equation. https://doi.org/10.1080/00036811.2023.2299714

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