• 论文 •

### 一类非线性等级结构种群控制模型解的适定性

1. 杭州电子科技大学运筹与控制研究所, 杭州 310018
• 出版日期:2019-08-25 发布日期:2019-12-05

HE Zerong,ZHANG Zhiqiang,WANG Shuping. The Well-Posedness of a Nonlinear Hierarchical Age-Structured Population Control Model[J]. Journal of Systems Science and Mathematical Sciences, 2019, 39(8): 1201-1211.

### The Well-Posedness of a Nonlinear Hierarchical Age-Structured Population Control Model

HE Zerong ,ZHANG Zhiqiang ,WANG Shuping

1. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018
• Online:2019-08-25 Published:2019-12-05

The objective of this paper is to analyze the basic properties for solutions of a nonlinear hierarchical age-structured population model, which is based on the assumption that the young individuals play a stronger role in the competition inside the population than the old ones. Firstly, we freeze up the nonlinear coefficients, transform the nonlinear system into a linear one and make some priori estimations for the solutions to the linear system. Then we define a solution mapping and show that the mapping has a unique fixed point, which is exactly the solution to the nonlinear model. Thirdly, we demonstrate that the population density depends continuously on the control variable, harvesting efforts, in the model by means of characteristics and integral estimations. The results obtained show that the model is well-posed, and lay a solid foundation to following researches such as the stability of steady states, controllability and variable optimal control problems.

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