Traveling waves solutions of isothermal chemical systems with decay

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Qi, Yuanwei^1,2 

[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[2] Shanxi Univ, Sch Math, Taiyuan 030006, Shanxi, Peoples R China

关键词: Microbial growth in a flow reactor;    Isothermal chemical systems with decay;    Traveling wave;    Existence;    Non-existence;   

DOI  :  10.1016/j.jde.2014.09.013

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free