周期变化环境中一类尺度结构种群系统的最优控制

Optimal Contraception Control for a Nonlinear Vermin Model with Size-Structure in a Periodic Environment

研究一类周期环境中具有尺度结构的非线性害鼠不育控制模型,其中控制变量同时出现在主方程和边界条件.首先利用冻结系数法和不动点理论证明模型非负解的存在唯一性,并给出状态关于控制变量的连续依赖性.接着利用共轭系统和切-法锥技巧导出最优性条件,再运用Ekeland变分原理证明最优不育策略的存在性.最后给出数值模拟结果,它表明:降低害鼠的繁殖率相对于增加其死亡率是预防鼠害发生的一种更为有效的方式.

In this paper,we investigate a periodic nonlinear size-structured vermin model with contraception control,in which the control variable appears in the principal equation and the boundary condition as well.Firstly,we establish the existence of a unique non-negative solution by means of frozen coefficients and fixed point theory,and show the continuous dependence of solutions on control variable.Next,adjoint system and tangent-normal cone techniques are used to obtain the optimality conditions.The existence of optimal contraception policy is verified by means of Ekeland's variational principle.Finally,some numerical results are presented,which shows that reducing the reproduction rate of the vermin is more effective than increasing its mortality to ease damages.