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Interaction of human migration and wealth distribution

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posted on 2017-05-10, 15:05 authored by V. Volpert, Sergei Petrovskii, A. Zincenko
Dynamics of human populations depends on various economical and social factors. Their migration is partially determined by the economical conditions and it can also influence these conditions. This work is devoted to the analysis of the interaction of human migration and wealth distribution. The model consists of a system of equations for the population density and for the wealth distribution with conventional diffusion terms and with cross diffusion terms describing human migration determined by the wealth gradient and wealth flux determined by human migration. Wealth production and consumption depend on the population density while the natality and mortality rates depend on the level of wealth. In the absence of cross diffusion terms, dynamics of solutions is described by travelling wave solutions of the corresponding reaction-diffusion systems of equations. We show persistence of such solutions for sufficiently small cross diffusion coefficients. This result is based on the perturbation methods and on the spectral properties of the linearized operators.

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Citation

Nonlinear Analysis: Theory, Methods and Applications, 2017, 159, pp. 408-423

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • AM (Accepted Manuscript)

Published in

Nonlinear Analysis: Theory

Publisher

Elsevier

issn

0362-546X

Acceptance date

2017-02-23

Copyright date

2017

Available date

2018-03-18

Publisher version

http://www.sciencedirect.com/science/article/pii/S0362546X17300743

Notes

The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above. Following the embargo period the above license will apply.

Language

en

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