Title

Propagation of Local Disturbances in Reaction Diffusion Systems Modeling Quadratic Autocatalysis

Authors

Authors

X. F. Chen;Y. W. Qi

Comments

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Abbreviated Journal Title

SIAM J. Appl. Math.

Keywords

quadratic autocatalysis; traveling wave; propagation of local; disturbance; reaction-diffusion; CUBIC AUTOCATALYSIS; TRAVELING-WAVES; FRONT SPEEDS; EQUATIONS; RATES; STABILITY; ENHANCEMENT; EXISTENCE; SHEARS; MEDIA; Mathematics, Applied

Abstract

This article studies the propagation of initial disturbance in a quadratic autocatalytic chemical reaction in one-dimensional slab geometry, where two chemical species A, called the reactant, and B, called the autocatalyst, are involved in the simple scheme A + B -> 2B. Experiments demonstrate that chemical systems for which quadratic or cubic catalysis forms a key step can support propagating chemical wavefronts. When the autocatalyst is introduced locally into an expanse of the reactant, which is initially at uniform concentration, the developing reaction is often observed to generate two wavefronts, which propagate outward from the initial reaction zone. We show rigorously that with such an initial setting the spatial region is divided into three regions by the two wavefronts. In the middle expanding region, the reactant is almost consumed so that A approximate to 0, whereas in the other two regions there is basically no reaction so that B approximate to 0. Most of the chemical reaction takes place near the wavefronts. The detailed characterization of the concentrations is given for each of the three zones.

Journal Title

Siam Journal on Applied Mathematics

Volume

69

Issue/Number

1

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

273

Last Page

282

WOS Identifier

WOS:000260847700013

ISSN

0036-1399

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