Pattern formation (II): The Turing Instability

Guo, Yan; Hwang, Hyung Ju

doi:10.1090/S0002-9939-07-08850-8

Pattern formation (II): The Turing Instability

Authors: Yan Guo and Hyung Ju Hwang
Journal: Proc. Amer. Math. Soc. 135 (2007), 2855-2866
MSC (2000): Primary 35K57, 35Pxx, 92Bxx
DOI: https://doi.org/10.1090/S0002-9939-07-08850-8
Published electronically: May 14, 2007
MathSciNet review: 2317962
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Abstract: We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the finite number of linear growing modes over a time scale of $\ln\frac{1}{\delta},$ where $\delta$ is the strength of the initial perturbation.

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