Spreading with two speeds and mass segregation in a diffusive competition system with free boundaries

TL;DR

This paper studies how two invasive species spread and segregate in a spherical environment, revealing that they spread at different speeds with populations concentrating in distinct regions over time.

Contribution

It introduces a model with two free boundaries for two competing species, analyzing their spreading speeds and mass segregation in a spherically symmetric setting.

Findings

Both species can successfully spread under certain conditions.

The species spread at different speeds, leading to population segregation.

The slower species concentrates in an expanding ball, while the faster species forms a shell outside it.

Abstract

We investigate the spreading behavior of two invasive species modeled by a Lotka-Volterra diffusive competition system with two free boundaries in a spherically symmetric setting. We show that, for the weak-strong competition case, under suitable assumptions, both species in the system can successfully spread into the available environment, but their spreading speeds are different, and their population masses tend to segregate, with the slower spreading competitor having its population concentrating on an expanding ball, say Bt, and the faster spreading competitor concentrating on a spherical shell outside Bt that disappears to infinity as time goes to infinity.