Aggregation in age and space structured population models: an asymptotic analysis approach

被引：11

作者：

Banasiak, J. ^{[1
,2
]}

Goswami, A. ^{[1
]}

Shindin, S. ^{[1
]}

机构：

[1] Univ KwaZulu Natal, Sch Math Sci, Durban, South Africa

[2] Tech Univ Lodz, Inst Math, PL-90924 Lodz, Poland

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2011年 / 11卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Structured population models; Aggregation; Singular perturbation; Asymptotic analysis; Semigroups; SEMIGROUPS;

D O I：

10.1007/s00028-010-0086-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we describe how techniques of asymptotic analysis can be used in a systematic way to perform 'aggregation' of variables, based on a separation of different time scales, in a population model with age and space structure. The main result of the paper is proving the convergence of the formal asymptotic expansion to the solution of the original equation. This result improves and clarifies earlier results of Arino et al. (SIAM J Appl Math 60(2):408-436, 1999), Auger et al. (Structured population models in biology and epidemiology. Springer Verlag, Berlin, 2008), Lisi and Totaro (Math Biosci 196(2):153-186, 2005).

引用

页码：121 / 154

页数：34

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