Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data

Abstract

This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial data are exponential decaying. By establishing a comparison principle for Hamilton-Jacobi equations, we are able to apply the Hamilton-Jacobi approach for Fisher-KPP equation due to Freidlin, Evans and Souganidis. As a result, the exact formulas of spreading speeds and their dependence on initial data are derived. Our results indicate that sometimes the spreading speed of the slower species is nonlocally determined. Connections of our results with the traveling profile due to Tang and Fife, as well as the more recent spreading result of Girardin and Lam, will be discussed.

References in corpus (2)

• Front propagation into unstable states
• Spreading speeds for one-dimensional monostable reaction-diffusion equations

Cited by in corpus (4)

• Stacked invasion waves in a competition-diffusion model with three species
• Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation
• Asymptotic spreading of KPP reactive fronts in heterogeneous shifting environments
• Sharp estimates for the spreading speed of the Lotka-Volterra diffusion system with strong competition