Abstract
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, DA and DB, are un- equal due to different molecular weights and/or sizes. Explicit bounds c∗ and c ∗ that depend on DB/DA 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.
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