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

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