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

    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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