Existence and nonexistence of travelling waves of a reaction-diffusion system

    Authors

    G. R. Liu;Y. W. Qi

    Comments

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    Abbreviated Journal Title

    J. Math. Anal. Appl.

    Keywords

    Iodate-arsenous-acid reaction; Applied electric field; Reaction-diffusion; Travelling wave; Existence; AUTOCATALYTIC REACTION FRONT; PROPAGATING FRONTS; IODATE OXIDATION; CHEMICAL WAVES; STABILITY; EQUATIONS; INSTABILITY; SPEEDS; ACID; Mathematics, Applied; Mathematics

    Abstract

    In this paper we study the existence and nonexistence of travelling waves of the reaction-diffusion system [GRAPHICS] , where a, b are concentration densities of the two chemical species, D > 0 is the ratio of diffusion coefficients of the two chemical species involved, E is the strength of the electric field applied, k > 0 is a parameter and g > I. The system arises from the study of two-dimensional iodate-arsenous-acid (IAA) reaction with a constant electric field applied. (IAA) reaction is very much studied in experiments and demonstrates the interesting phenomenon of instability driven by buoyancy of travelling waves. By using a novel approach, explicit bounds c(*)(D, E) and c* (D, E) are derived such that there is a unique travelling wave of every speed c > = c*(D, E) and there does not exist any travelling wave of speed c < c(*)(D, E), with q being fixed. In addition, c*(D, E) bears a close resemblance of the minimum travelling wave speed of the classical case of D = 1 and E = 0, when 0 < E << 1 and D similar to 1. (C) 2013 Published by Elsevier Inc.

    Journal Title

    Journal of Mathematical Analysis and Applications

    Volume

    401

    Issue/Number

    1

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    130

    Last Page

    139

    WOS Identifier

    WOS:000314739000013

    ISSN

    0022-247X

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