Maximal muliplicity of the critical points of the CR equation modeling a constant flow stirred tank reactor
type: Item
instance of: scholarly article
title: Maximal muliplicity of the critical points of the CR equation modeling a constant flow stirred tank reactor
zbMATH Open document ID: 0656.76089
DOI: 10.1016/0022-247X(87)90003-5
author: S. H. Smith
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: We use the work of \textit{M. Golubitsky} and \textit{B. Keyfitz} [SIAM J. Math. Anal. 11, 316-339 (1980; Zbl 0448.58001)] and \textit{M. Golubitsky} and \textit{D. G. Schaeffer} [Singularities and groups in bifurcation theory (1985; Zbl 0607.35004)] to establish the existence of seven steady states. We also show that if seven steady states exist for the nonadiabatic case there also must exist seven steady states for the adiabatic case. Of course, it would be desirable to establish whether or not the upper bound for the maximum number of critical point is always realized for any number of consecutive reactions. However, the present method does not appear to generalize to the higher dimensional situations. We discuss the difficulties that are encountered in trying to apply this method to higher dimensional cases. Finally we present criteria for the existence of non-physical critical points and classify when the various possible numbers of critical points occur in terms of values of the process parameters.
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 80A32
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4072634
zbMATH Keywords: chemical reaction
zbMATH Keywords: steady states
MaRDI profile type: Publication
cites work: Dynamics of the CR equations modeling a constant flow stirred tank reactor
cites work: A Qualitative Study of the Steady-State Solutions for a Continuous Flow Stirred Tank Chemical Reactor
cites work: Singularities and groups in bifurcation theory. Volume I
cites work: Classification and Unfolding of Sequential Bifurcations
cites work: A theory for imperfect bifurcation via singularity theory
full work available at URL: 0022-247x(87)90003-5
OpenAlex ID: W1975876225
description: scientific article; zbMATH DE number 4072634