Nonlinear Stability Analysis of Stationary Solutions for a Special Class of Reaction-Diffusion Systems with Respect to Small Perturbations

We prove that the stationary solution of a class of reaction-diffusion systems is stable in the intersection of the Sobolev space 1 (ℝ) and an exponentially weighted space 1 (ℝ).Particular attention is given to a special case, the combustion model.The stationary solution considered here is the end state of the traveling front associated with the system, and thus the present result complements recent work by A. Ghazaryan, Y. Latushkin and S. Schecter, where the stability of the traveling fronts was investigated.