Global stability in a two-species attraction-repulsion system with competitive and nonlocal kinetics (Q6612567)

A chemotactic system describing two competing species is considered in bounded smooth domains of \(\mathbb R^n\) under the homogeneous Neumann boundary conditions. The reaction terms are bilinear and involve masses of both populations. The system consists of two nonlinear parabolic equations for the evolution of populations, and two either elliptic or parabolic equations for chemicals. Results on the global-in-time existence and boundedness of solutions are proved, as well as their exponential decay to homogeneous states, under suitable restrictions on parameters.