Title

Existence And Nonexistence Of Travelling Waves Of A Reaction-Diffusion System

Keywords

Applied electric field; Existence; Iodate-arsenous-acid reaction; Reaction-diffusion; Travelling wave

Abstract

In this paper we study the existence and nonexistence of travelling waves of the reaction-diffusion system {at=axx-Eax-ab-kabq,bt=Dbxx-DEbx+ab+kabq, where a, b are concentration densities of the two chemical species, D>0 is the ratio of diffusion coefficients of the two chemical species involved, E is the strength of the electric field applied, k>0 is a parameter and q>1. The system arises from the study of two-dimensional iodate-arsenous-acid (IAA) reaction with a constant electric field applied. (IAA) reaction is very much studied in experiments and demonstrates the interesting phenomenon of instability driven by buoyancy of travelling waves. By using a novel approach, explicit bounds c*(D, E) and c*(D, E) are derived such that there is a unique travelling wave of every speed c≥c*(D, E) and there does not exist any travelling wave of speed c

Publication Date

5-1-2013

Publication Title

Journal of Mathematical Analysis and Applications

Volume

401

Issue

1

Number of Pages

130-139

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmaa.2012.09.060

Socpus ID

84872956515 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84872956515

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