Reaction-diffusion waves in an isothermal chemical system with general orders of autocatalysis and spatial dimension

The possibility of initiating reaction-diffusion waves in an autocatalytic system represented schematically byAB, ratekab^p (p >- 1, witha, b being the concentrations ofA andB respectively) is considered through the local input ofB, measured by the parameter ₀, into an otherwise uniform expanse ofA. It is shown that for 1 <-p < 1 + (2/N) (whereN is the space dimension) waves develop no matter how small the value of ₀, while forp > 1 + (2/N) there is some threshold value of ₀ below which waves are not formed, with diffusion playing the dominant role throughout. A lower bound for this threshold value is found. The permanent-form travelling wave equations are then discussed and the behaviour of the solution asp 1 is considered in detail. It is shown that a three-region structure develops with the asymptotic wave speedv being singular (of the formv 2–2.3381 (p- 1)^2/3) asp 1.