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

被引：2

作者：

Banasiak, Jacek ^{[1
,2
]}

Goswami, Amartya ^{[3
]}

Shindin, Sergey ^{[1
]}

机构：

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

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

[3] Univ Zululand, Dept Math Sci, Richards Bay, South Africa

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2014年 / 11卷 / 02期

关键词：

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

D O I：

10.1007/s00009-013-0319-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：533 / 559

页数：27

共 21 条

[1]

[Anonymous], 1995, SINGULARLY PERTURBED

[2]

[Anonymous], 1979, Introduction to dynamic systems: theory, models, and applica-tions

[3]

Arino O, 2000, SIAM J APPL MATH, V60, P408

[4]

Bailey NTJ, 1964, ELEMENTS STOCHASTIC

[5] Chapman-Enskog asymptotic procedure in structured population dynamics [J].

Banasiak, J. ;

Shindin, S. .

NUOVO CIMENTO C-COLLOQUIA AND COMMUNICATIONS IN PHYSICS, 2010, 33 (01) :31-38

[6] Aggregation in age and space structured population models: an asymptotic analysis approach [J].

Banasiak, J. ;

Goswami, A. ;

Shindin, S. .

JOURNAL OF EVOLUTION EQUATIONS, 2011, 11 (01) :121-154

[7]

Banasiak J., 2009, GAKUTO INT SER MATH, V31, P221

[8]

Banasiak J., SINGULARLY PER UNPUB

[9] Relative entropy and discrete Poincare inequalities for reducible matrices [J].

Banasiak, Jacek ;

Namayanja, Proscovia .

APPLIED MATHEMATICS LETTERS, 2012, 25 (12) :2193-2197

[10] Interplay between degenerate convergence of semigroups and asymptotic analysis: a study of a singularly perturbed abstract telegraph system [J].

Banasiak, Jacek ;

Bobrowski, Adam .

JOURNAL OF EVOLUTION EQUATIONS, 2009, 9 (02) :293-314

← 1 2 3 →