Existence and nonexistence of travelling waves of a reaction-diffusion system

In this paper we study the existence and nonexistence of travelling waves of the reaction-diffusion system [GRAPHICS] , where a, b are concentration densities of the two chemical species, D > 0 is the ratio of diffusion coefficients of the two chemical species involved, E is the strength of the electric field applied, k > 0 is a parameter and g > I. The system arises from the study of two-dimensional iodate-arsenous-acid (IAA) reaction with a constant electric field applied. (IAA) reaction is very much studied in experiments and demonstrates the interesting phenomenon of instability driven by buoyancy of travelling waves. By using a novel approach, explicit bounds c(*)(D, E) and c* (D, E) are derived such that there is a unique travelling wave of every speed c >= c*(D, E) and there does not exist any travelling wave of speed c < c(*)(D, E), with q being fixed. In addition, c*(D, E) bears a close resemblance of the minimum travelling wave speed of the classical case of D = 1 and E = 0, when 0 < E << 1 and D similar to 1. (C) 2013 Published by Elsevier Inc.