Singularly perturbed population models with reducible migration matrix 1. Sova-Kurtz theorem and the convergence to the aggregated model

Jacek Banasiak; Amartya Goswami

doi:10.3934/dcds.2015.35.617

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2015, Volume 35, Issue 2: 617-635. Doi: 10.3934/dcds.2015.35.617

This issue Previous Article Analytic semigroups and some degenerate evolution equations defined on domains with corners Next Article Classical operators on the Hörmander algebras

Singularly perturbed population models with reducible migration matrix 1. Sova-Kurtz theorem and the convergence to the aggregated model

Jacek Banasiak^1, and
Amartya Goswami^2,

1.
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban
2.
Department of Mathematical Sciences, University of Zululand

Received: December 31, 2012

Revised: December 31, 2013

Published: January 2015

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Abstract

Multiple time scales are common in population models with age and space structure, where they are a reflection of often different rates of demographic and migratory processes. This makes the models singularly perturbed and allows for their aggregation which, while significantly reducing their complexity, does not alter their essential dynamic properties. There are several methods of aggregation of such models. In this paper we shall show how the Trotter-Kato-Sova-Kurtz theory developed to analyze convergence of $C_0$-semigroups can be used in this field. The paper also extends some of the previous results by considering reducible migration matrices which are important in modelling populations living in geographically patched areas with restricted communication between the patches.

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Mathematics Subject Classification: Primary: 92D25, 35B25, 47D06; Secondary: 35Q92, 47N20.

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