一类具有加权总规模的非线性种群扩散系统的最优控制

Optimal Control for a Class of Nonlinear Weighted Size Population Diffusion System

讨论了一类与年龄相关的非线性种群扩散系统的最优控制问题,其生死率依赖于个体年龄和加权总规模.利用不动点原理确立了系统的适定性,借助于法锥概念得到了控制问题最优解存在的必要条件.这些结果可为种群扩散系统最优控制问题的实际研究提供理论基础.

This paper discussed the optimal control problem for a class of nonlinear agedependent population diffusion system with fertility and mortality depending on a weighted size. Well-posedness of the system is examined via fixed point theorem. By the conception of normal cone, first order necessary conditions for the problem are obtained. These results can provide a theoretical basis for the practical study of the optimal control problems in age-dependent population system with diffusion.