Stability of pulsating fronts for bistable reaction-diffusion equations in spatially periodic media

The first part of the paper is concerned with the asymptotic stability of pulsating fronts in R N for spatially periodic bistable reaction-diffusion equations with respect to decaying perturbations. Precisely, we show that the solution u ( t, x ) of the initial value problem converges to the pulsating front as t -> + infinity uniformly in R N . In the second part, we investigate the existence and asymptotic behavior of the entire solution u ( t, x ) emanating from a pulsating front for the equation in exterior domains. The proof of the asymptotic behavior is relying on the application of the proof for the stability of the pulsating front. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.