The existence of traveling wave front solutions of a model of the Belousov-Zhabotinskii chemical reaction

Abstract

The boundary value problem ∂u ∂t′ = u(1 − u − rv) + ∂ 2u ∂x′ 2 ∂v ∂t′ = − buv + ∂ 2y ∂x′ 2 where u(− ∞, t′) = v(∞, t′) = 0 and v(− ∞, t′) = u(∞, t′) = 1 for each t′ > 0 has been proposed by Murray as a model for the Belousov-Zhabotinskii chemical reaction. Here u and v are proportional to the concentrations of bromous acid and bromide ion, respectively. We prove that there is a range of values for b and r over which the boundary value problem has traveling wave front solutions.