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• W2564270989 abstract "In this paper, we study an attraction-repulsion Keller-Segel chemotaxis model with logistic source begin{document}$begin{cases} u_{t}=Δ u-χnabla·(unabla v)+ξnabla·(unabla w)+f(u), &x∈Ω, t>0, v_{t}=Δ v+α u-β v, &x∈Ω, t>0, w_{t}=Δ w+γ u-δ w, &x∈Ω, t>0,end{cases};;;;(*)$ end{document} in a smooth bounded domain $Ω subset mathbb{R}^n(n≥ 1)$, 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 begin{document}$f(u)≤ a-bu^θ, u≥ 0, mathrm{with~some} a≥ 0,b>0,θ≥1.$ end{document} 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 begin{document}$begin{cases} θ > max{1,3-frac6n}, &text{when } 1≤ n≤ 5, θ≥ 2, &text{when } 6≤ n≤ 9, θ>1+frac{2(n-4)}{n+2}, &text{when} n≥10.end{cases}$ end{document} Furthermore, when $f(u)=μ u(1-u)$ and repulsion cancels attraction, by constructing appropriate Lyapunov functional, we show that if $μ>frac{χ^2α^2(β-δ)^2}{8δβ^2}$, the solution $(u,v,w)$ exponentially stabilizes to the constant stationary solution $(1,frac{α}{β},frac{γ}{δ})$ 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." @default.
• W2564270989 created "2017-01-06" @default.
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• W2564270989 date "2017-01-01" @default.
• W2564270989 modified "2023-09-24" @default.
• W2564270989 title "Boundedness and large time behavior of an attraction-repulsion chemotaxis model with logistic source" @default.
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• W2564270989 doi "https://doi.org/10.3934/krm.2017034" @default.
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