Second-order optimality conditions for the bilinear optimal control of a degenerate equation
arXiv:2212.11046 · doi:10.1080/00036811.2023.2299714
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.
19 pages