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Stability and characteristic wavelength of planar interfaces in the large diffusion limit of the inhibitor

Published online by Cambridge University Press:  14 November 2011

Masaharu Taniguchi  and
Yasumasa Nishiura
Masaharu Taniguchi
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01, Japan
Yasumasa Nishiura
Affiliation:
Laboratory of Nonlinear Studies and Computation, Research Institute for Electronic Science, Hokkaido University, Sapporo 060, Japan
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Abstract

A characteristic wavelength and its parametric dependency are studied for planar interfaces of activator-inhibitor systems as well as their stability in two-dimensional space. When an unstable planar interface is slightly perturbed in a random way, it develops with a characteristic wavelength, that is, the fastest-growing one. A natural question is to ask under what conditions this characteristic wavelength remains finite and approaches a positive definite value as the width of interface, say ε, tends to zero. In this paper, we show that the fastest-growing wavelength has a positive limit value as ε tends to zero for the system:

This is a fundamental fact for stuyding the domain size of patterns in higher-space dimensions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 1 , 1996 , pp. 117 - 145
Copyright
Copyright © Royal Society of Edinburgh 1996

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