Global bifurcation and structure of Turing patterns in the 1-D Lengyel-Epstein model
type: Item
instance of: scholarly article
title: Global bifurcation and structure of Turing patterns in the 1-D Lengyel-Epstein model
zbMATH Open document ID: 1072.35091
author: Jaeduck Jang
author: Wei-Ming Ni
author: Moxun Tang
published in: Journal of Dynamics and Differential Equations
publication date: 2005-03-15T00:00:00Z
review text: The authors study the analytical aspects of the Lengyel-Epstein reaction diffusion system that models the formation of the so-called Turing patterns (or more generally non-constant steady states) in the chlorine dioxide reaction. After recalling some relevant results from their earlier paper, the authors provide a detailed discussion of the global bifurcation structure of the set of the non-constant steady states focusing on the one-dimensional case. The discussed bifurcation theory approach relies on results due to Crandall and Rabinowitz, the Rabinowitz global bifurcation theorem and the Leray-Schauder degree theory. Moreover, the limiting behavior of the solution set is analytically described by an appropriate use of the solution to the corresponding shadow system.
reviewed by: Wojciech Kryszewski
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 92E20
zbMATH DE Number: 2145891
zbMATH Keywords: CIMA reaction
zbMATH Keywords: open chemical systems
zbMATH Keywords: Lengye-Epstein model
zbMATH Keywords: shadow systems
zbMATH Keywords: non-constant steady states
zbMATH Keywords: one-dimensional case
zbMATH Keywords: Rabinowitz global bifurcation theorem
zbMATH Keywords: Leray-Schauder degree theory
MaRDI profile type: Publication
full work available at URL: s10884-004-2782-x
OpenAlex ID: W1996333888
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DOI: 10.1007/S10884-004-2782-X
description: scientific article; zbMATH DE number 2145891