具分布观测的年龄相关的种群扩散系统生育率控制的非线性问题  

Non-linear Problem of the Fertility Rate Control for Age-dependent Population Diffusion System with Distributed Observation

作　　者：李健全[1] 陈任昭[2] 

机构地区：[1]华南师范大学数学科学学院,广州510631 [2]东北师范大学数学科学学院,长春130024

出　　处：《工程数学学报》2006年第5期801-815,共15页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10471021);广东省自然科学基金(031496);华南师范大学博士启动基金(670070)

摘　　要：本文讨论了具分布观测的年龄相关的种群扩散系统最优生育率控制的非线性问题,证明了系统解的存在唯一性和最优生育率控制的存在性,得到了控制为最优的一阶必要条件及其由偏微分方程组和变分不等式组成的最优性组,并进而建立了最优生育率控制的反馈表达式。这些结果可为种群扩散系统中的最优控制问题的实际研究提供理论基础。The non-linear problem of the optimal fertility rate control for age-dependent population diffusion system with distributed observation is discussed. The existence and uniqueness of the solution and the existence of the optimal fertility rate control for the system are proved. The first-order necessary conditions for a control to be optimal and its optimality systems consisting of the partial differential equations and variational inequality are obtained. Furtherly, the feed-back formula of expression for an optimal control is established. These results can provide a theoretical basis for the pratical study of the optimal control problems in population diffusion system.

关 键 词：年龄相关的种群扩散系统 分布观测 最优生育率控制 非线性问题 最优性组 反馈控制 

分 类 号：O231.4[理学—运筹学与控制论]