关键词: 抛物系统, 最优控制, Neumann边界条件, 竞争模型

Abstract: 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.

Key words: parabolic system; , optimal control, Neumann boundary condition, competition model