种内竞争模型的最优控制问题  

Optimal Control Problem of Intraspecific Competition Model

作　　者：那杨 王宏越 杜润梅 NA Yang;WANG Hongyue;DU Runmei(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,长春130012

出　　处：《吉林大学学报（理学版）》2024年第2期243-248,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12071067;12161045;12026219);吉林省科技发展计划项目(批准号:20220101033JC)。

摘　　要：考虑一类在Neumann边界条件下具有抛物系统种内竞争的最优控制问题.首先在该系统中讨论种群内部的竞争关系和种群间的交互作用,将目标泛函定义为捕捞得到的利润;其次证明该系统最优控制存在的必要条件,并给出最优控制的表达式.We considered the optimal control problem for a class of intraspecific competition with parabolic systems under Neumann boundary conditions.Firstly,we discussed the competition relationships within the population and the interactions between the populations in the system,and defined the objective functional as the profit obtained from harvesting.Secondly,we proved the necessary condition for the existence of the optimal control in the system,and gave an expression for the optimal contorl.

关 键 词：抛物系统 最优控制 NEUMANN边界条件 竞争模型 

分 类 号：O175.26[理学—数学]