Sharp estimates for the spreading speeds of the Lotka-Volterra competition-diffusion system: the strong-weak type

TL;DR

This paper provides precise asymptotic estimates for the spreading speeds in a two-species Lotka-Volterra competition-diffusion system under strong-weak competition, especially when the minimal wave speed is not linearly determined.

Contribution

It establishes sharp estimates for spreading speeds in complex scenarios where minimal wave speeds are nonlinearly determined, advancing understanding of invasion dynamics.

Findings

Derived asymptotic behavior for invasive-native species interactions.

Analyzed cases with two invasive species.

Provided sharp estimates for nonlinearly determined wave speeds.

Abstract

We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is not linear determined, we establish the precise asymptotic behavior of the solution of the Cauchy problem in two different situations: (i) one species is an invasive one and the other is a native species; (ii) both two species are invasive species.