Extension to Systems of Fisher-Kolmogorov Equations. Example: A Simple Model for an Ionic Autocatalytic System
Part of the Springer Monographs in Mathematics book series (SMM)
In this chapter we extend the approach developed in the previous chapters to determine the large-t structure of scalar reaction-diffusion equations of the Fisher-Kolmogorov tpye by considering a system of Fisher-Kolmogorov equations. This system arises as a simple model for an isothermal, autocatalytic, chemical reaction scheme. The scheme is based on the autocatalytic step
. Here a and b are the concentrations of the reactant , A, and th e autocatalyst, B, respectively, k is the reaction rate constant and n the general order of autocatalysis, (n ≥ 1).
$$ A + nB \to (n + 1)B, rate = kab^n . $$
KeywordsAsymptotic Solution Unstable Manifold Region Versus Initial Value Problem Minimum Speed
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