Convergence and Traveling Wave Solutions in a Delayed Diffusive Competitive Model

This paper studies the convergence and minimal wave speed of traveling wave solutions in a delayed competitive model. Due to the effect of time delays, this system may not satisfy the classical comparison principle. When the domain is bounded and equipped with homogeneous Neumann boundary condition, we obtain the persistence and stability of any positive mild solutions by constructing proper contracting rectangles. When the domain is whole space R, we study the minimal wave speed of traveling wave solutions by presenting the existence or nonexistence of nontrivial traveling wave solutions with any wave speeds, which models the coinvasion-coexistence of these species. Our main recipe on minimal wave speed is the generalized upper and lower solutions, contracting rectangles and spreading speeds.