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数学进展 - 2020, Vol. 49(6): 713-722
研究论文
年龄等级结构两种群系统模型解的存在唯一性
Existence and Uniqueness of Solutions for a Hierarchical Two Age-structured Population System

何泽荣*, 周楠, 韩梦杰
HE Zerong, ZHOU Nan, HAN Mengjie

杭州电子科技大学运筹与控制研究所, 杭州, 浙江, 310018
Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, P. R. China

收稿日期: 2019-09-03
出版日期: 2020-11-17
2020, Vol. 49(6): 713-722
DOI: 10.11845/sxjz.2019097b


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摘要 本文提出一类新的显示等级差异的两种群系统框架模型, 它是具有全局反馈边界条件的偏微分-积分方程组, 能描述种群内部和种群之间的竞争、合作、捕食等各种关系. 基于一组较为自然的参数条件, 运用不动点方法建立了无穷时域中模型非负解的存在唯一性, 借助特征线和积分不等式导出解对初始年龄分布的一致连续性. 所获结果为研究系统稳定性、能控性及各类最优控制问题奠定了基础.
关键词 年龄等级种群系统偏微分--积分方程组存在唯一性不动点    
Abstract:We propose a class of new hierarchical model for the evolution of two interacting age-structured populations, which is a system of integro-partial differential equations with global feedback boundary conditions and may describe the interactions such as competition, cooperation and predator-prey relation. Based upon a group of natural conditions, the existence and uniqueness of solutions on infinite time interval are proved by means of fixed point and extension principle, and the continuous dependence of the solution on the initial age distribution is established. These results lay a sound basis for the investigation of stability, controllability and variable optimal control problems.
Key wordshierarchy of ages    population system    system of integro-partial differential equations    existence and uniqueness    fixed points
PACS:  O175.29  
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