Coupled reaction-diffusion waves in an isothermal autocatalytic chemical system

The initiation and propagation of reaction-diffusion travelling waves in two regions coupled together by the linear diffusive interchange of the autocatalytic species is considered via an initial-value problem in which amounts of the autocatalyst are introduced locally into otherwise uniform concentrations of the other species. The reaction in one region is given by quadratic autocatalysis, while the reaction in the other is given by quadratic autocatalysis together with the linear decay of the autocatalyst. A priori bounds for the initial-value problem are obtained first. These, together with the solution valid for small inputs of the autocatalyst, enable conditions to be derived under which travelling waves can be initiated giving a wave for all γ with k0 = √2 [2-k-2γ+ (k2+4γ2)1/2]1/2.