BOUNDEDNESS AND PERSISTENCE OF POPULATIONS IN ADVECTIVE LOTKA-VOLTERRA COMPETITION SYSTEM

We are concerned with a two-component reaction-advection- diffusion Lotka-Volterra competition system with constant diffusion rates subject to homogeneous Neumann boundary conditions. We first prove the global existence and uniform boundedness of positive classical solutions to this system. This result complements some of the global existence results in [Y. Lou, M. Winkler and Y. Tao , SIAM J. Math. Anal., 46 (2014), 1228-1262.], where one diffusion rate is taken to be a linear function of the population density. Our second result proves that the total population of each species admits a positive lower bound, under some conditions of system parameters (e.g., when the intraspecific competition rates are large). This result of population persistence indicates that the two competing species coexist over the habitat in a long time.