Optimal Control for Age Distribution and Weighted Size Competitive Species in a Polluted Environment  

污染环境中具有年龄分布和加权竞争种群的最优控制

作　　者：WANG Zhanping 王战平(宁夏大学数学统计学院,宁夏银川750021)

机构地区：[1]School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China

出　　处：《应用数学》2024年第4期1014-1026,共13页Mathematica Applicata

基　　金：Supported by the Natural Science Foundation of Ningxia(2023AAC03114);National Natural Science Foundation of China(72464026).

摘　　要：In the paper,we study an optimal control for a system representing a competitive species model with fertility and mortality depending on a weighted size in a polluted environment.A fixed point theorem is applied to obtain the existence and uniqueness exhibited by a non-negative solution of above mentioned model.A maximum principle helps to carefully verify the existence of the optimal control policy,and tangent-normal cone techniques help to obtain the optimal condition specific to control issue.本文研究污染环境中生育率和死亡率依赖于加权大小的竞争种群模型的最优控制问题.应用不动点定理得到了上述模型非负解的存在性和唯一性.借助极大值原理验证了最优控制策略的存在性,利用法锥性质获得了针对控制问题的最优条件.

关 键 词：Optimal control Competitive species POLLUTION Maximum principle 

分 类 号：O231.4[理学—运筹学与控制论]