污染环境下具有加权总规模的非线性时变种群扩散系统的最优边界控制  

Optimal Boundary Control of Nonlinear Time-varying Population Diffusion System with Weighted Total Size in Polluted Environment

作　　者：苏琳 许泽宇 SU Lin;XU Ze-yu(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《兰州文理学院学报（自然科学版）》2020年第6期21-27,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：讨论了一类基于毒素作用和加权总规模的非线性时变种群扩散系统的最优边界控制问题.由于环境污染导致种群扩散系统受到毒素的影响,又考虑到生死率依赖于加权总规模,借助Banach不动点定理和比较定理得到该系统存在唯一的非负解,同时利用极小化序列及紧性定理证明最优解的存在性.A class of nonlinear time-varying population diffusion system based on toxin effect and weighted total scale in a polluted environment was discussed.Owing to the environmental pollution,the population diffusion system was affected by toxin,and considering that the rate of life and death depended on the weighted total scale,the unique non-negative solution of the system was obtained by means of Banach fixed-point theorem and comparison theorem.Furthermore,the minimization sequence and compactness theorem were used to prove the existence of the optimal solution.

关 键 词：污染环境 加权总规模 年龄结构 最优边界控制 扩散 

分 类 号：O175.1[理学—数学]