Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The development of travelling waves in quadratic and cubic autocatalysis with unequal diffusion rates. III. Large time development in quadratic autocatalysis


Authors: J. Billingham and D. J. Needham
Journal: Quart. Appl. Math. 50 (1992), 343-372
MSC: Primary 92E20; Secondary 80A32
DOI: https://doi.org/10.1090/qam/1162280
MathSciNet review: MR1162280
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Abstract: We study the isothermal, quadratic autocatalytic reaction scheme $ A + \\ B \to 2B$ , where $ A$ is a reactant and $ B$ is an autocatalyst. We consider the situation when a quantity of $ B$ is introduced locally into a uniform expanse of $ A$ in one-dimensional slab geometry. By analysing the large time asymptotic solution of the resulting initial value problem we show that either a permanent form travelling wave or a phase wave develops. In the case when a travelling wave evolves we determine the first two terms in the large time asymptotic expansion of the propagation speed, which is dependent upon the asymptotic form of the initial input distribution of $ B$ far ahead of the wavefront.


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DOI: https://doi.org/10.1090/qam/1162280
Article copyright: © Copyright 1992 American Mathematical Society


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