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Title: Interaction of human migration and wealth distribution
Authors: Volpert, V.
Petrovskii, Sergei
Zincenko, A.
First Published: 18-Mar-2017
Publisher: Elsevier
Citation: Nonlinear Analysis: Theory, Methods and Applications, 2017, 159, pp. 408-423
Abstract: 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.
DOI Link: 10.1016/
ISSN: 0362-546X
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2017. This article is distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License ( ), which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Description: 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.
Appears in Collections:Published Articles, Dept. of Mathematics

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