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Diffusion driven instability in an inhomogeneous circular domain


May, A and Firby, PA and Bassom, AP, Diffusion driven instability in an inhomogeneous circular domain, Mathematical and Computer Modelling, 29, (4) pp. 53-66. ISSN 0895-7177 (1999) [Refereed Article]

Copyright Statement

Copyright 1999 Elsevier

DOI: doi:10.1016/S0895-7177(99)00039-4


Classical reaction-diffusion systems have been extensively studied and are now well understood. Most of the work to date has been concerned with homogeneous models within one-dimensional or rectangular domains. However, it is recognised that in most applications nonhomogeneity, as well as other geometries, are typically more important. In this paper, we present a two chemical reaction-diffusion process which is operative within a circular region and the model is made nonhomogeneous by supposing that one of the diffusion coefficients varies with the radial variable. Linear analysis leads to the derivation of a dispersion relation for the point of onset of instability and our approach enables both axisymmetric and nonaxisymmetric modes to be described. We apply our workings to the standard Schnackenberg activator-inhibitor model in the case when the variable diffusion coefficient takes on a step-function like profile. Some fully nonlinear simulations show that the linear analysis captures the essential details of the behaviour of the model.

Item Details

Item Type:Refereed Article
Keywords:two chemical reaction, Schnackenberg model, step-live diffusivity
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108523
Year Published:1999
Web of Science® Times Cited:5
Deposited By:Mathematics and Physics
Deposited On:2016-04-21
Last Modified:2016-08-03

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