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Extension to Systems of Fisher-Kolmogorov Equations. Example: A Simple Model for an Ionic Autocatalytic System

  • J. A. Leach
  • D. J. Needham
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

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
$$ A + nB \to (n + 1)B, rate = kab^n . $$
(1)
. 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).

Keywords

Asymptotic Solution Unstable Manifold Region Versus Initial Value Problem Minimum Speed 
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Copyright information

© Springer-Verlag London 2004

Authors and Affiliations

  • J. A. Leach
    • 1
  • D. J. Needham
    • 1
  1. 1.Department of MathematicsThe University of ReadingReadingUK

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