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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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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Additional Information

Yan Guo
Affiliation: Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
Email: guoy@dam.brown.edu

Hyung Ju Hwang
Affiliation: School of Mathematics, Trinitiy College Dublin, Dublin 2, Ireland & Department of Mathematics, Postech, Pohang 790-784, Korea
Email: hjhwang@postech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08850-8
PII: S 0002-9939(07)08850-8
Received by editor(s): October 19, 2005
Received by editor(s) in revised form: May 26, 2006
Published electronically: May 14, 2007
Communicated by: Walter Craig
Article copyright: © Copyright 2007 American Mathematical Society