The stability of traveling wave solutions for a diffusive competition system of three species

In this article, we investigate the stability of monotone traveling wave solutions for a diffusive three species competition system. By considering the initial perturbations of the traveling waves in some weighted function spaces, the monotone three-species waves become asymptotically stable. Further stability will be determined from the asymptotic behavior of the waves. This can be achieved by using the method of super- and subsolutions.