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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 where 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:
https://doi.org/10.1090/S0002-9939-07-08850-8

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