论文标题
双线性对退化方程的最佳控制的二阶最佳条件
Second-order optimality conditions for the bilinear optimal control of a degenerate equation
论文作者
论文摘要
本文的主要目的是研究强烈退化抛物线方程双线性控制的二阶最佳条件。该方程在空间结构域的边界处退化。建立了状态方程的适当性以及较弱的最大原则。我们证明了控制对状态运营商的某些可不同性能以及最佳解决方案的存在。最后，我们为系统提供一阶和二阶最优条件。
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.
