Existence and uniqueness of solutions for a hierarchical system of two age-structured populations

doi:10.3868/S140-DDD-023-004-X

Frontiers of Mathematics in China

2023, Vol. 18

Issue (1): 51-62 https://doi.org/10.3868/S140-DDD-023-004-X

本期目录

Existence and uniqueness of solutions for a hierarchical system of two age-structured populations

Zerong HE(

), Nan ZHOU, Mengjie HAN

Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018, China

全文: PDF(396 KB) HTML

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 words： Hierarchy of ages population system integro-partial differential equations existence and uniqueness fixed points

出版日期: 2023-05-31

Corresponding Author(s): Zerong HE

引用本文:

. [J]. Frontiers of Mathematics in China, 2023, 18(1): 51-62.
Zerong HE, Nan ZHOU, Mengjie HAN. Existence and uniqueness of solutions for a hierarchical system of two age-structured populations. Front. Math. China, 2023, 18(1): 51-62.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.3868/S140-DDD-023-004-X
https://academic.hep.com.cn/fmc/CN/Y2023/V18/I1/51

1	A S Ackleh, K Deng. Monotone approximation for a hierarchical age-structured population model. Dynamics of Continuous, Dyn Contin Discrete Impuls Syst Ser B Appl Algorithms 2005; 12(2): 203–214
2	A S Ackleh, K Deng, u S Hu. A quasilinear hierarchical size-structured model: well-posedness and approximation. Appl Math Optim 2005; 51(1): 35–59
3	S Aniţa. Analysis and Control of Age-Dependent Population Dynamics. Dordrecht: Kluwer Academic Publishers, 2000
4	À Calsina, J Saldaña. Asymptotic behaviour of a model of hierarchically structured population dynamics. J Math Biol 1997; 35(8): 967–987
5	À Calsina, J Saldaña. Basic theory for a class of models of hierarchically structured population dynamics with distributed states in the recruitment. Math Model Methods Appl Sci 2006; 16(10): 1695–1722
6	J M Cushing. The dynamics of hierarchical age-structured populations. J Math Biol 1994; 32(7): 705–729
7	J M Cushing, J Li. Oscillations caused by cannibalism in a size-structured population model. Canad Appl Math Quart 1995; 3(2): 155–172
8	D A Dewsbury. Dominance rank, copulatory behavior, and differential reproduction. Q Rev Biol 1982; 57(2): 135–159
9	Z He, H Chen, g S Wang. The global dynamics of a discrete nonlinear hierarchical population system. Int J Biomath 2019; 12(2): 1950022
10	Z He, D Ni, u Y Liu. Theory and approximation of solutions to a harvested hierarchical age-structured population model. J Appl Anal Comput 2018; 8(5): 1326–1341
11	Z He, D Ni, g S Wang. Control problem for a class of hierarchical population system. J Systems Sci Math Sci 2018; 38(10): 1140–1148
12	S M Henson, J M Cushing. Hierarchical models of intra-specific competition: scramble versus contest. J Math Biol 1996; 34(7): 755–772
13	M IannelliF Milner. The Basic Approach to Age-Structured Population Dynamics. Dordrecht: Springer, 2017
14	S R-J Jang, J M Cushing. A discrete hierarchical model of intra-specific competition. J Math Anal Appl 2003; 280: 102–122
15	E A Kraev. Existence and uniqueness for height structured hierarchical population model. Natur Resource Modeling 2001; 14(1): 45–70
16	Y Liu, e Z R He. On the well-posedness of a nonlinear hierarchical size-structured population model. ANZIAM J 2017; 58: 482–490
17	A Lomnichi. Individual differences between animals and the natural regulation of their numbers. J Animal Ecology 1978; 47(2): 461–475
18	J Shen, C W Shu, g M Zhang. A high order WENO scheme for a hierarchical size-structured population model. J Sci Comput 2007; 33(3): 279–291

Viewed

Full text

Abstract

Cited

Shared

Discussed