Large time behavior of solutions to a quasilinear attraction-repulsion chemotaxis model with nonlinear secretion

In this paper, we study the large time behavior of a quasilinear attraction-repulsion chemotaxis model with nonlinear secretion: u(t) = del. (D(u) del u - chi phi(u) del v + xi psi(u) del w) + lambda u - mu u(epsilon); 0=triangle v-alpha 1v+beta 1u gamma 1; 0=triangle w-alpha 2w+beta 2u gamma 2, x epsilon Omega omega, t > 0. We show that the global-in-time bounded smooth solution of the system converges exponentially/algebraically to steady state in the large time limit. Those results generalize some of our previous results [G. Ren and B. Liu, Math. Models Methods Appl. Sci. 30(13), 2619-2689 (2020) and G. Ren and B. Liu, J. Differ. Equations 268(8), 4320-4373 (2020)]. Published under an exclusive license by AIP Publishing.