Stability of Traveling Waves for a Class of Reaction-Diffusion Systems That Arise in Chemical Reaction Models

Stability results are proved for traveling waves in a class of reaction-diffusion systems that arise in chemical reaction models. The class includes systems in which there is no diffusion in some equations. A weight function that decays exponentially at one end is required to stabilize the essential spectrum. Perturbations of the wave in H1 or BUC that are small in both the weighted norm and the unweighted norm are shown to stay small in the unweighted norm and to decay exponentially to a shift of the traveling wave in the weighted norm. Perturbations that are in addition small in the L1 norm decay algebraically to a shift of the wave in the L∞ norm. A decomposition of the variables that yields a triangular structure for the linearization at one end of the wave is exploited to prove the results. An application to exothermic-endothermic reactions is given.