Semi-waves and spreading speeds of stage-structured diffusive competition model with a free boundary

A stage-structured diffusive competition model with a free boundary is considered. The main aim of this paper is to study the evolution of the mature invasive species with competitive ability, and determine whether it disrupts the stable ecosystem provided by native species. According to the long-time behaviors under the case of weak-strong competition, strong-weak competition and weak competition, we obtain respectively the exact asymptotic spreading speed by delay-induced semi-wave problems if the spreading of invasive species occurs. And we demonstrate that, as the moving coefficient goes to infinite, the corresponding Cauchy problem can be viewed as the limiting profile of model and the asymptotic spreading speed approaches the minimal speed of the corresponding traveling wavefront solutions. Moreover, under strong-weak competition situation, the asymptotic spreading speed of invasive species is decreasing with respect to the maturation time. Mathematics Subject Classification 35K57, 35R35, 35B40, 92D25