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

Abstract

A stage-structured diffusive competition model with a free boundary is considered. The main aim of this paper is to study the evolutions of 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 the model, and the asymptotic spreading speed approaches the minimal speed of the corresponding traveling wavefront solutions. Moreover, under the strong-weak competition situation, the asymptotic spreading speed of invasive species will decrease when the maturation time is longer.