Existence Of Traveling Waves Of Auto-Catalytic Systems With Decay

Keywords

Autocatalytic chemical systems; Microbial growth and competition; Traveling wave

Abstract

This article establishes the existence of traveling waves of a class of reaction–diffusion systems which model the pre-mixed isothermal autocatalytic chemical reaction of order m (m>1) between two chemical species, a reactant and an auto-catalyst, and a linear decay. Moreover, our result shows that the set of speed is contained in a bounded interval for any fixed initial value at x=−∞. This is in strong contrast to either the reaction–diffusion systems of autocatalytic chemical reaction of the order m without decay, or to the systems which have the same order of decay, which were shown by various authors (e.g. [8,13,17,26]) that the set of traveling wave speeds contains [c⁎,∞) for some c⁎>0. The same systems also appear in a mathematical model of microbial growth and competition in a flow reactor; see [2,24].

Publication Date

6-5-2016

Publication Title

Journal of Differential Equations

Volume

260

Issue

11

Number of Pages

7982-7999

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jde.2016.02.009

Socpus ID

84961221302 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84961221302

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