Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616951 | Journal of Mathematical Analysis and Applications | 2013 | 10 Pages |
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