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

Source abstract

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 $H^1$ 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 $L^1$ norm decay algebraically to a shift of the wave in the $L^\infty$ 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.