The global self-similarity of a chemical reaction system with critical nonlinearity

    Authors

    Y. W. Qi

    Comments

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    Abbreviated Journal Title

    Proc. R. Soc. Edinb. Sect. A-Math.

    Keywords

    UNEQUAL DIFFUSION RATES; FORM TRAVELING-WAVES; CUBIC AUTOCATALYSIS; ORDER AUTOCATALYSIS; COMBUSTION SYSTEM; MODEL; Mathematics, Applied; Mathematics

    Abstract

    In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u(1,t)=u(1,xx) - u(1)u(2)(2), u(2,t)=du(2,xx)+u(1)u(2)(2) with non-negative initial data, where the constant d > 0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as vertical bar x vertical bar -> infinity. In particular, we show that, for a substantial class of L-1 initial data, the exact large-time behaviour of solutions is characterized by a universal, non-Gaussian spatio-temporal profile, subject to the apparent conservation of total mass.

    Journal Title

    Proceedings of the Royal Society of Edinburgh Section a-Mathematics

    Volume

    137

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    867

    Last Page

    883

    WOS Identifier

    WOS:000249023800010

    ISSN

    0308-2105

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