Sharp estimates for the spreading speed of the Lotka-Volterra diffusion system with strong competition

TL;DR

This paper establishes precise spreading speeds and profiles for the classical two-species Lotka-Volterra diffusion system under strong competition, using novel supersolution and subsolution constructions.

Contribution

It provides the first sharp estimates for the spreading speed and profile in strong competition Lotka-Volterra systems.

Findings

Determined exact spreading speeds for invasive and native species scenarios.

Constructed optimal supersolutions and subsolutions for the system.

Established the dynamical behavior and profiles of solutions.

Abstract

This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one and the other is a native one or both are invasive species. Our results seem to be the first that provide a precise spreading speed and profile for such a strong competition system. Among other things, our analysis relies on the construction of new types of supersolution and subsolution, which are optimal in certain sense.