Free boundary problems for the competitive Lotka-Volterra system

Abstract

Abstract. In this paper we investigate two free boundary problems for a Lotka-Volterra type competition
model in one space dimension. The main objective is to understand the asymptotic behavior of the two
competing species spreading via a free boundary. We prove a spreading-vanishing dichotomy, namely the
two species either successfully spread to the right-half-space as time goes to infinity and survive in the
new environment, or they fail to establish and die out in the long run.