Global existence and asymptotic behavior of solutions to a chemotaxis system with chemicals and prey-predator terms (Q784297)

The author studies a chemotaxis-competition system consisting of two parabolic equations with Lotka-Volterra reaction and cross-diffusion terms coupled with two elliptic equations for diffusion of two chemicals. Under some assumptions on the coefficients global-in-time solutions are shown to converge to homogeneous steady states. Arguments used to show asymptotic stability are based on comparison principles and invariant regions approach as well as a priori estimates of energy and entropy type.