Second-order optimality conditions for the bilinear optimal control of a degenerate equation
Optimization and Control
2024-11-07 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2212.11046,
title = {Second-order optimality conditions for the bilinear optimal control of a degenerate equation},
author = {Cyrille Kenne and Landry Djomegne and Pascal Zongo},
journal= {arXiv preprint arXiv:2212.11046},
year = {2024}
}
Comments
19 pages