污染环境中具有年龄结构的非线性时变种群扩散系统的最优控制  

Optimal Control for Age-Structured Nonlinear Time-Varying Population Diffusion System in a Polluted Environment

作　　者：贠晓菊 王战平 YUN Xiaoju;WANG Zhanping(School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《应用数学》2018年第3期621-630,共10页Mathematica Applicata

基　　金：宁夏高等学校科学研究项目(NGY2015048);宁夏大学研究生创新项目(GIP2017046)

摘　　要：本文研究污染环境中具有年龄结构的非线性时变种群扩散系统的最优控制问题.利用不动点定理得到该系统非负解的存在性和唯一性.利用极小化序列及紧性证明最优控制的存在性.利用法锥性质,得到最优控制的必要性条件.In this paper, we study the optimal control issue for age-structured nonlinear timevarying population diffusion system in a polluted environment. The existence and uniqueness of nonnegative solution for this model is obtained by using the fixed point theorem. The existence of optimal control policy is verified by using the minimum principle and compactness. The necessary conditions for the control problem are given by applying the tangent-normal cone techniques.

关 键 词：污染环境 非线性 时变种群扩散系统 最优控制 极小化序列 

分 类 号：O231.4[理学—运筹学与控制论]