Traveling Waves Solutions Of Isothermal Chemical Systems With Decay

Keywords

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

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≠n. A typical system in autocatalysis is A+2B→3B (with rate k1ab2) and B→C (with rate k2b), where m=2 and n=1, involving two chemical species, a reactant A and an auto-catalyst B whose diffusion coefficients, DA and DB, 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 k1 and k2 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 DB/DA, traveling speed c and rate constants k1, k2. On the other hand, it is proved that there exists no traveling wave when one of the chemical species is immobile, DB=0 or n>m for all choices of other parameters.

Publication Date

2-1-2015

Publication Title

Journal of Differential Equations

Volume

258

Issue

3

Number of Pages

669-695

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jde.2014.09.013

Socpus ID

84919471669 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84919471669

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