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 autocatal ytic system represented schematically by A --> B, rate kab(p) (p great er-than-or-equal-to 1, with a, b being the concentrations of A and B r espectively) is considered through the local input of B, measured by t he parameter beta0, into an otherwise uniform expanse of A. It is show n that for 1 less-than-or-equal-to p < 1 + (2/N) (where N is the space dimension) waves develop no matter how small the value of beta0, whil e for p > 1 + (2/N) there is some threshold value of beta0 below which waves are not formed, with diffusion playing the dominant role throug hout. A lower bound for this threshold value is found. The permanent-f orm travelling wave equations are then discussed and the behaviour of the solution as p --> 1 is considered in detail. It is shown that a th ree-region structure develops with the asymptotic wave speed v being s ingular (of the form upsilon approximately 2 - 2.3381 (p - 1)2/3) as p --> 1.