Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms

This paper demonstrates the existence of a minimum wave speed for reaction diffusion systems whose permanent form travelling wave solutions satisfy th e nonlinear ordinary differential equation u" + cu' + f(u, u'; c) = 0 when there are two equilibrium points, one of which is not hyperbolic, unde r certain restrictions on the behaviour off. It also shows how to construct a trapping region in the phase plane, which leads to an upper bound on the value of the minimum wave speed. This class of systems includes autocataly tic reactions of order greater than one and combustion waves in premixed ga seous and solid fuels.