Volume 49, Issue 2
The Traveling Wave of Auto-Catalytic Systems-Monotone and Multi-Peak Solutions

Y. Qi


J. Math. Study, 49 (2016), pp. 149-168.

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  • 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, $D_A$ 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.

  • History

Published online: 2016-07

  • AMS Subject Headings

34C20, 34C25, 92E20

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