Steady-state solution for a general Schnakenberg model
type: Item
instance of: scholarly article
title: Steady-state solution for a general Schnakenberg model
zbMATH Open document ID: 1231.35069
author: Yan Li
published in: Nonlinear Analysis. Real World Applications
publication date: 2011-06-24T00:00:00Z
review text: The author studies the Schnakenberg model of chemical reaction with limit cycle behaviour. The reactants are distributed in an isolated domain. The elliptic nonlinear system describes the steady-state distributions of the reactants. The boundary conditions are homogeneous Neumann conditions. This system has a unique constant solution. The author reveals the conditions (on the diffusivities of reactants) of uniqueness of this solution and of existence of non-constant solutions. In particular, it is shown that no non-constant solution is possible provided that the diffusivity of one reactant is high enough. Conditions on the existence of such solution are given in terms of eigenvalues of the Laplace operator with boundary conditions in the domain.
reviewed by: Ilya A. Chernov
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 80A30
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
zbMATH DE Number: 5912743
zbMATH Keywords: Schnakenberg model
zbMATH Keywords: chemical kinetics
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: implicit function theorem
zbMATH Keywords: topological degree
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2010.12.014
OpenAlex ID: W1969364481
cites work: Stationary Pattern of a Ratio-Dependent Food Chain Model with Diffusion
cites work: Positive steady-state solutions of the Noyes--Field model for Belousov--Zhabotinskii reaction.
cites work: Non-constant positive steady states of the Sel'kov model.
cites work: Diffusion, self-diffusion and cross-diffusion
DOI: 10.1016/J.NONRWA.2010.12.014
description: scientific article; zbMATH DE number 5912743