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

Masaharu Taniguchi, Yasumasa Nishiura

Research output: Contribution to journalArticle

9 Citations (Scopus)

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: ut = Δu + ε-2f(u, v), vt = ε-1 Δv + g(u, v). This is a fundamental fact for stuyding the domain size of patterns in higher-space dimensions.

Original languageEnglish
Pages (from-to)117-145
Number of pages29
JournalRoyal Society of Edinburgh - Proceedings A
Volume126
Issue number1
DOIs
Publication statusPublished - Jan 1 1996
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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