Title

The development of travelling waves in cubic auto-catalysis with different rates of diffusion

Authors

Authors

Y. W. Qi

Comments

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Abbreviated Journal Title

Physica D

Keywords

cubic auto-catalysis; travelling wave; minimum speed; reaction-diffusion; ISOTHERMAL CHEMICAL-SYSTEM; PROPAGATING FRONTS; STABILITY; EXISTENCE; EQUATIONS; DECAY; ACID; Mathematics, Applied; Physics, Multidisciplinary; Physics, Mathematical

Abstract

In this paper we study the isothermal auto-catalytic chemical reaction, A + 2B -> 3 B involving two chemical species A and B. Their diffusion coefficients, denoted by D-A and D-B, respectively, are unequal, which happens when the two chemical species have different molecular weights. The propagating reaction-diffusion waves that may develop from a local initial input of the auto-catalyst, B, are investigated in one spatial dimension. We show the existence of travelling wave solutions for all propagation speed v >= v(2)*, with v(2)* a function of the ratio of the diffusion 2 2 rates of the species A and B, representing the estimated minimum propagation speed. Our result improves significantly on the results of early works. In addition, we show the non-existence of travelling wave solutions when v <= v(2), where v(2) depends on the ratio of the diffusion rates of the species A and B. We believe that our non-existence result is the first of the kind for equations of the isothermal auto-catalytic chemical reaction type. We also demonstrate similar results on the general isothermal auto-catalytic chemical reaction, A + nB -> (n + 1) B, of n-th order with it > 1. (c) 2006 Elsevier B.V. All rights reserved.

Journal Title

Physica D-Nonlinear Phenomena

Volume

226

Issue/Number

2

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

129

Last Page

135

WOS Identifier

WOS:000244572500003

ISSN

0167-2789

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