具logistic增长的边界退化抛物系统的最优控制

Optimal control for boundary-degenerate parabolic equations with logistic growth

本文研究具有logistic增长的边界退化抛物系统的最优控制问题.首先建立弱解的适定性,在此基础上得到目标泛函最优控制的存在性和稳定性;然后对最优系统进行刻画,把最优控制通过对偶系统的解表示出来.

This paper deals with the optimal control problem of a parabolic control system with the logistic growth and the boundary degeneracy.We firstly establish the well-posedness of weak solutions.Then the existence and the stability of the optimal control that minimizes the cost functional are proved.Moreover,the optimal control is characterized in terms of the unique solution of the optimality system,which consists of the state equation coupled with the adjoint equation.