The existence and non-existence of travelling front in high order auto-catalysis chemical reaction

    Authors

    Y. W. Qi;G. R. Liu

    Comments

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    Abbreviated Journal Title

    Sci. China-Math.

    Keywords

    high order autocatalysis; travelling wave; minimum speed; reaction-diffusion; REACTION-DIFFUSION SYSTEMS; CUBIC AUTOCATALYSIS; PROPAGATING FRONTS; WAVES; STABILITY; EQUATIONS; COMBUSTION; MODEL; ACID; Mathematics, Applied; Mathematics

    Abstract

    This article studies propagating wave fronts in an isothermal chemical reaction A+nB - > (n+1)B involving two chemical species, a reactant A and an auto-catalyst B whose diffusion coefficients, D (A) and D (B) , are unequal due to different molecular weights and/or sizes. More accurate bounds v* and v* that depend on D (B) /D (A) , when the ratio is less than 1, are derived such that there is a unique travelling wave of every speed v a (c) 3/4 v* and there does not exist any travelling wave of speed v < v*. The refined bounds for D (B) /D (A) < 1 case is compatible to what has been shown in earlier work for D (B) /D (A) > 1 when n a (c) 3/4 3.

    Journal Title

    Science China-Mathematics

    Volume

    55

    Issue/Number

    9

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    1761

    Last Page

    1768

    WOS Identifier

    WOS:000307817900002

    ISSN

    1674-7283

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