Abstract
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).
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The work of all authors was supported by the National Research Foundation of South Africa under grant FA2007030300001 and the University of KwaZulu-Natal Research Fund.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Banasiak, J., Goswami, A. & Shindin, S. Aggregation in age and space structured population models: an asymptotic analysis approach. J. Evol. Equ. 11, 121–154 (2011). https://doi.org/10.1007/s00028-010-0086-7
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DOI: https://doi.org/10.1007/s00028-010-0086-7