Title: Stability analysis of Reaction-Diffusion Systems with constant coefficients on growing domains

Authors: Anotida Madzvamuse

Addresses: Department of Mathematics, University of Sussex, Mantell Building, Brighton, BN1 9RF, UK

Abstract: We present stability theory for reaction-diffusion systems with constant coefficients on growing domains. The model equations on growing domains are transformed to fixed domains at each time yielding a conservative system. We derive and show that the diffusion-driven instability conditions for an exponentially growing domain depend on the domain growth rate. By looking at the eigenvalues, we show that the shifting of the Turing space is equivalent to the standard Turing space on a fixed domain but with eigenvalues shifted to the left of the complex plane by a constant factor given by the divergence of the domain velocity.

Keywords: diffusion-driven instability; convection-reaction-diffusion systems; Turing instability; pattern formation; growing domains; divergence free; mesh movement; ALE formulation; stability analysis; reaction-diffusion Systems; constant coefficients.

DOI: 10.1504/IJDSDE.2008.023002

International Journal of Dynamical Systems and Differential Equations, 2008 Vol.1 No.4, pp.250 - 262

Published online: 06 Feb 2009 *

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