Abstract
This paper is concerned with the long time behavior of bounded solutions to a two-species time-periodic Lotka-Volterra reaction-diffusion system with strong competition. It is well known that solutions of the Cauchy problem of this system with front-like initial values converge to a bistable periodic traveling front. One may ask naturally how solutions of such time-periodic systems with other types of initial data evolve as time increases. In this paper, by transforming the system into a cooperative system on [0, 1], we first show that if the bounded initial value ?(x) has compact support and equals 1 for a sufficiently large x-level, then solutions converge to a pair of diverging periodic traveling fronts. As a by-product, we obtain a sufficient condition for solutions to spread to 1. We also prove that if the two species are initially absent from the right half-line x > 0 and the slower one dominates the faster one on x < 0, then solutions approach a propagating terrace, which means that several invasion speeds can be observed.
