  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 entire space as time t goes to infinity and
survive in the new environment, or they fail to establish and die out in the
long run. The long time behavior of the solutions and criteria for spreading
and vanishing are also obtained. This paper is an improvement and extension of
J. Guo and C. Wu.
