Multiple steady states in a simple reaction–diffusion model with Michaelis–Menten (first-order Hinshelwood–Langmuir) saturation law: The limit of large separation in the two diffusion constants

Abstract

The admissible multiple nonuniform steady states of a model bimolecular autocatalytic reaction–diffusion system with Michaelis–Menten (first-order Hinshelwood–Langmuir) saturation law are constructed in the case of large scale separation in the two diffusion constants. Both the Dirichlet and the Neumann problems are discussed in a one-dimensional geometry, and the corresponding bifurcation pictures are given.