Theory of propagation of discontinuities in kinetic systems with multiple time scales: Fronts, front multiplicity, and pulses

Abstract

We consider a reaction–diffusion system far from chemical equilibrium, with kinetics on multiple time scales and the capacity of attaining one or multiple homogeneous stable steady states. For such systems we present a theory of the structure (concentration profile) and velocity of fronts based on a matched asymptotic solution of the singular perturbation problem. We analyze single front (wave) propagation as a transition occurs from one stable stationary state to another; show the possibility of multiple mode front propagation; and discuss single pulse propagation in systems with one stable stationary state. For each process we confirm the theory by comparison with numerical solutions of the coupled differential equations for a model system. Finally, by application of the theory we discuss a reduction of the complexity of the stability analysis of these fronts.