Asymptotic speeds of spreading for the Lotka-Volterra system with strong competition in $\mathbb{R}^N$

TL;DR

This paper investigates the long-term spreading speeds of solutions to the Lotka-Volterra competition system in multi-dimensional space, revealing how initial conditions influence the asymptotic propagation rates.

Contribution

It provides the first comprehensive analysis of asymptotic spreading speeds for the Lotka-Volterra system with strong competition in ^N, linking initial conditions to spreading dynamics.

Findings

Derived asymptotic spreading speeds for two initial condition types

Showed dependence of spreading speeds on scalar front speeds

Established connections between scalar and system spreading behaviors

Abstract

This paper is concerned with the asymptotic spreading behavior of solutions of the Lotka-Volterra system with strong competition in $\mathbb{R}^{N}$. Two types of initial conditions are proposed: (C1) two species initially occupy bounded domains; (C2) two species initially occupy the whole space separately. The spreading dynamics for (C1) (C2) is strongly depending on the speeds of traveling fronts of the scalar equations with no competition and the system. We give the asymptotic speeds of spreading for both (C1) (C2).