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

摘要

This paper demonstrates the existence of a minimum wave speed for reaction diffusion systems whose permanent form travelling wave solutions satisfy the nonlinear ordinary differential equation u"+cu'+f(u,u';c)=0 when there re two equilibrium points, one of which is not hyperbolic, under certain restrictions on the behaviour of f. 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 autocatalytic reactions of order greater than one and combustion waves in premixed gaseous and solid fuels.