Title

Traveling waves solutions of isothermal chemical systems with decay

Authors

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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