Traveling waves solutions of isothermal chemical systems with decay

    Authors

    Y. W. Qi

    Comments

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    Abbreviated Journal Title

    J. Differ. Equ.

    Keywords

    Microbial growth in a flow reactor; Isothermal chemical systems with; decay; Traveling wave; Existence; Non-existence; BIO-REACTOR MODEL; CRITICAL NONLINEARITY; CUBIC AUTOCATALYSIS; SELF-SIMILARITY; STEADY-STATES; DYNAMICS; PROPAGATION; Mathematics

    Abstract

    This article studies propagating traveling waves in a class of reaction diffusion systems which include a model of microbial growth and competition in a flow reactor proposed by Smith and Zhao [17], and isothermal autocatalytic systems in chemical reaction of order m with a decay order n, where m and n are positive integers and m not equal n. A typical system in autocatalysis is A + 2B - > 3B (with rate k(1) ab(2)) and B - > C (with rate k(2)b), where m = 2 and n = 1, 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. Here a is the concentration density of A, b that of B and C an inert chemical species. The two constants k(1) and k(2) are material constants measuring the relative strength of respective reactions. It is shown that there exist traveling waves when m > 1 and n = 1 with suitable relation between the ratio D-B/D-A, traveling speed c and rate constants k(1), k(2). On the other hand, it is proved that there exists. no traveling wave when one of the chemical species is immobile, D-B =0 or n > m for all choices of other parameters. (C) 2014 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Differential Equations

    Volume

    258

    Issue/Number

    3

    Publication Date

    1-1-2015

    Document Type

    Article

    Language

    English

    First Page

    669

    Last Page

    695

    WOS Identifier

    WOS:000347268100002

    ISSN

    0022-0396

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