A model for the diffusion of populations in annular patchy environments

Cui, G.; Freedman, H. I.

doi:10.1090/qam/1686193

Authors: G. Cui and H. I. Freedman
Journal: Quart. Appl. Math. 57 (1999), 339-354
MSC: Primary 92D25; Secondary 35Q80, 92D40
DOI: https://doi.org/10.1090/qam/1686193
MathSciNet review: MR1686193
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Abstract: A system of reaction-diffusion differential equations is utilized to model the diffusion of a population through annular patches with different carrying capacities. In the case of continuous solutions with continuous flux, it is shown that a unique, positive steady-state solution exists. In the case of radially symmetric initial conditions, it is shown that all solutions of the Cauchy problem approach this steady-state solution. Models involving nonsymmetric initial conditions are also considered.

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