THE TRAVELING WAVE OF AUTO-CATALYTIC SYSTEMS – THE LIMITING CASES

This article studies propagating  wave of a reaction-diffusion system modeling auto-catalytic  chemical reaction $ A + n B \rightarrow (n + 1) B$ 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.

We are investigating the extreme cases of  $ D \equiv D_B/D_A \ll 1$ or $ D \gg 1$.

We reformulate the traveling wave problem of general case to derive explicit bounds  of speed for existence and non-existence.