Reaction-Diffusion Waves in a Simple Isothermal Chemical System

  • J. H. Merkin
  • D. J. Needham
Part of the Research Reports in Physics book series (RESREPORTS)


Previous work on reaction-diffusion waves in the simple isothermal autocatalytic systems
$$\begin{array}{*{20}{c}} {quadratic:}&{A + B \Rightarrow 2B}&{rate}&{{k_1}ab} \end{array}$$
$$\begin{array}{*{20}{c}} {cubic:}&{A + 2B \Rightarrow 3B}&{rate}&{{k_2}a{b^2}} \end{array}$$
(and mixed schemes combining (la) and (lb)) has assumed that the catalyst B can exist indefinitely, see, for example [1–8]. Here we allow for the finite lifetime of catalyst B which we assume decays to the inert product C via
$$\begin{array}{*{20}{c}} {linear:}&{B \Rightarrow C}&{rate}&{{k_2}b} \end{array}$$
$$\begin{array}{*{20}{c}} {quadratic:}&{B + B \Rightarrow C}&{rate}&{{k_q}{b^2}} \end{array}$$
(here a and b are the concentrations of A and B and the ki are the rate constants).


Wave Speed Travel Wave Solution Confluent Hypergeometric Function Finite Lifetime Lead Order Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • J. H. Merkin
    • 1
  • D. J. Needham
    • 2
  1. 1.School of MathematicsUniversity of LeedsLeedsUK
  2. 2.School of MathematicsUniversity of East AngliaNorwichUK

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