具年龄和加权的半线性种群系统的最优边界控制

摘要

The authors discussed the optimal boundary control for a semi-linear age dependent population system based on weight, proved the existence of optimal boundary control via Mazur's theorem. We obtained the necessary conditions for an optimal control, using Gateax differentiation and Lions' theory of variational inequalities; and then obtained the optimality system consisting of integral paritial differential equation and variational inequalities. The optimality system can determine optimal control. These results may serve as theoretical reference for practical researches of the control problem in population systems. Its optimality systems determine the optimal control.%讨论一类具年龄和加权的半线性种群系统的最优控制问题.运用Mazur's定理证明了最优边界控制的存在性,利用G(a)teax微分和Lions的变分不等式理论得到了控制为最优的一阶必要条件,从而得到了由积分偏微分方程和变分不等式构成的最优性组,该最优性组能确定最优控制.