(untitled) (Journal of Mathematical Study, 2016)
This article studies propagating wave fronts of a reaction-diffusion system modeling an isothermal chemical reaction A+2B → 3B involving two chemical species, a reactant A and an auto-catalyst B, whose diffusion coefficients, D_A and D_B, are unequal due to different molecular weights and/or sizes. Explicit bounds c_∗ and c^∗ that depend on D_B/D_A are derived such that there is a unique travelling wave of every speed c ≥ c^∗ and there does not exist any travelling wave of speed c < c_∗. Furthermore, the reaction-diffusion system of the Gray-Scott model of A+2B → 3B, and a linear decay B → C, where C is an inert product is also studied. The existence of multiple traveling waves which have distinctive number of local maxima or peaks is shown. It shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different traveling pulses.