BOUNDEDNESS AND LARGE TIME BEHAVIOR OF AN ATTRACTION-REPULSION CHEMOTAXIS MODEL WITH LOGISTIC SOURCE

摘要

In this paper, we study an attraction-repulsion Keller-Segel chemotaxis model with logistic source in a smooth bounded domain Ω ? R~n (n ≥ 1), with homogeneous Neumann boundary conditions and nonnegative initial data (u_0, v_0, w_0) satisfying suitable regularity, where χ ≥ 0, ξ ≥ 0, α, β, γ, δ >0 and f is a smooth growth source satisfying f(0) ≥ 0 and When χα = ξγ (i.e. repulsion cancels attraction), the boundedness of classical solution of system (?) is established if the dampening parameter θ and the space dimension n satisfy Furthermore, when f(u) = μu(1 ? u) and repulsion cancels attraction, by constructing appropriate Lyapunov functional, we show that if, the solution (u, v, w) exponentially stabilizes to the constant stationary solution in the case of 1 ≤ n ≤ 9. Our results implies that when repulsion cancels attraction the logistic source play an important role on the solution behavior of the attraction-repulsion chemotaxis system.