Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

Jacek Banasiak; Amartya Goswami; Sergey Shindin

doi:10.1007/s00009-013-0319-4

Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

Jacek Banasiak, Amartya Goswami, Sergey Shindin

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.

Original language	English
Pages (from-to)	533-559
Number of pages	27
Journal	Mediterranean Journal of Mathematics
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s00009-013-0319-4
Publication status	Published - May 2014
Externally published	Yes

Keywords

aggregation
asymptotic analysis
Chapman-Enskog asymptotic expansion
initial layer
multiple time scales
Reducible matrices
semigroups
singular perturbation
Structured population models

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-013-0319-4

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abstract = "The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.",

keywords = "aggregation, asymptotic analysis, Chapman-Enskog asymptotic expansion, initial layer, multiple time scales, Reducible matrices, semigroups, singular perturbation, Structured population models",

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AU - Goswami, Amartya

AU - Shindin, Sergey

PY - 2014/5

Y1 - 2014/5

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AB - The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.

KW - aggregation

KW - asymptotic analysis

KW - Chapman-Enskog asymptotic expansion

KW - initial layer

KW - multiple time scales

KW - Reducible matrices

KW - semigroups

KW - singular perturbation

KW - Structured population models

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JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 2

ER -

Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

Abstract

Keywords

ASJC Scopus subject areas

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