Stacked invasion waves in a competition-diffusion model with three species

We investigate the spreading properties of a three-species competition-diffusion system, which is not order-preserving. We apply the Hamilton-Jacobi approach, due to Freidlin, Evans and Souganidis, to establish upper and lower estimates of spreading speed for the slowest species, which turn out to be dependent on the spreading speeds of the two faster species. The estimates we obtained are sharp in some situations. The spreading speed is being characterized as the free boundary point of the viscosity solution for certain variational inequality cast in the space of speeds. To the best of our knowledge, this is the first theoretical result on three-species competition system in unbounded domains.