Abstract

In this talk, I will present recent so called “Unity is not strength” results proved by Grégoire Nadin and myself. We investigated two-species competition-diffusion systems in which the interspecific competition is strong and diffusion rates are different and wondered which species would asymptotically prevail. We addressed this question in the particular case of front-like initial data connecting one extinction state to the other, or in other words we obtained the sign of the speed of the bistable invasion fronts. Firstly, I will explain how the result is deduced in the case of space-homogeneous media, where the fronts are classical traveling waves and where the result is entirely sharp. Secondly, I will explain how the result can be extended to the case of space-periodic media, where the fronts are pulsating fronts, whose existence is actually a priori unclear but was also addressed, and where the result is “almost” sharp.