BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR IN A QUASILINEAR TWO-SPECIES CHEMOTAXIS SYSTEM WITH LOOP

Chemotaxis is the directed movement of cells or organisms in response to the gradients of concentration of the chemical stimuli, plays essential roles in various biological process. In this paper, we consider a quasilinear two-species chemotaxis-competition system with loop in higher dimensions defined on a smooth bounded domain with homogeneous Neumann boundary conditions. With the help of suitable energy functional and some estimates, we obtain the global existence and boundedness of the classical solution of the model, and also show the large time behavior and convergence rate of the solution. Our results show that the nonlinear diffusion mechanism has an inhibitory effect on the blow-up of solution and partially generalized some results in the literature.