POSITIVE SOLUTIONS IN THE COMPETITIVE LOTKA-VOLTERRA REACTION-DIFFUSION MODEL WITH ADVECTION TERMS

This paper is mainly devoted to the existence and uniqueness, and especially the global asymptotical stability of the coexistence steady state for a competitive Lotka-Volterra reaction-diffusion model with advection term arising in ecology. Our approaches utilized here include the monotone dynamical systems theory, the sub-super solutions method, the principal spectral theory, and some other nontrivial analytic skills.

Automated summary

This paper focuses on the existence, uniqueness, and global asymptotical stability of the coexistence steady state for a competitive Lotka-Volterra reaction-diffusion model with advection term in ecology. The approaches utilized include monotone dynamical systems theory, sub-super solutions method, principal spectral theory, and other nontrivial analytic skills.