分析一类具有个体年龄等级差异的非线性种群系统模型解的适定性问题. 运用特征线法、积分不等式和不动点原理证明了系统非负解的存在唯一性和有界性, 以及解对控制变量的一致连续性. 拓展了常见的年龄结构系统基本理论, 为研究种群的长期演化和调控问题奠定基础.

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.