年龄相关的种群系统的最优扩散控制

The Optimal Diffusion Control for Age-dependent Population Systems

运用扰动方法研究了由积分-偏微分方程所描述的年龄相关的种群系统的最优扩散控制问题.首先,在证明了原系统及其扰动系统正则广义解存在唯一等预备结果的基础上,用先验估计和紧性定理,证明了系统最优扩散控制的存在性.其次,利用Gteax微分和变分不等式等理论,得到了控制为最优的必要条件和由偏微分方程与变分不等式所构成的最优性组,由最优性组确定最优控制.

The optimal diffusion control problem for the age dependent population systems represented by integral differential equations is disussed by using perturbation method. First,the existence of the optimal diffussion control for the system is proved by prior estimates and compactmess theoremon,on the basis of the regularite generalized solution of the primary system and the perturbation existence and uniqueness. Next,the necessary condition for a control to be optimal and the optimality system are deduced, using Gateax differentiation and Lions＇s theory of variational inequalities;and then the optimal system consisting of integral partial differential equations and variational inequalities. The optimal system can determine optimal controls.