Maximal muliplicity of the critical points of the CR equation modeling a constant flow stirred tank reactor
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.
scientific article; zbMATH DE number 4072634