Article ID Journal Published Year Pages File Type
4616951 Journal of Mathematical Analysis and Applications 2013 10 Pages PDF
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>0D>0 is the ratio of diffusion coefficients of the two chemical species involved, EE is the strength of the electric field applied, k>0k>0 is a parameter and q>1q>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)c∗(D,E) and c∗(D,E)c∗(D,E) are derived such that there is a unique travelling wave of every speed c≥c∗(D,E)c≥c∗(D,E) and there does not exist any travelling wave of speed c

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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