Asymptotic Behavior of Solutions for Competitive Models with Free Boundaries

In this paper, we study a competitive model involving two species. When the competition is strong enough, the two species are separated by a free boundary. If the initial data has a positive bound at infinity. We prove that the solution will converge, as $t\to \mathrm{\infty }$, to the traveling wave solution and the free boundary will move to infinity with a constant speed.