Large time behavior of solution to an attraction-repulsion chemotaxis system with logistic source in three dimensions

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• 作者：Dan Li^a ; ^{liwadanj@126.com} ; Chunlai Mu^a ; ^{clmu2005@163.com} ; Ke Lin^a ; ^{shuxuelk@126.com} ; Liangchen Wang^b ; ^{wanglc@cqupt.edu.cn}
• 关键词：Chemotaxis ; Attraction&ndash ; repulsion ; Boundedness ; Logistic source ; Asymptotic behavior
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：914-936
• 全文大小：451 K
• 卷排序：448

文摘

This paper studies the attraction–repulsion chemotaxis system with logistic source ut=Δu−χ∇⋅(u∇v)+ξ∇⋅(u∇w)+f(u)ut=Δu−χ∇⋅(u∇v)+ξ∇⋅(u∇w)+f(u), vt=Δv−α1v+β1uvt=Δv−α1v+β1u, wt=Δw−α2w+β2uwt=Δw−α2w+β2u in a smooth bounded convex domain Ω⊂R3Ω⊂R3, subject to nonnegative initial data and homogeneous Neumann boundary conditions, where χ, ξ  , αiαi and βiβi(i=1,2)(i=1,2) are positive parameters and the logistic source function f   fulfills f(s)=s−μsγ+1,s≥0,μ>0andγ≥1. It is shown that this system possesses a unique global bounded classical solution under the conditions αi≥12 and μ≥max⁡{(412χβ1+9ξβ2)γ,(9χβ1+412ξβ2)γ}. Furthermore, whenever u0≢0u0≢0 and for any γ∈Nγ∈N, the solution of the system approaches to the steady state ((1μ)1γ,(1μ)1γβ1α1,(1μ)1γβ2α2) in the norm of L∞(Ω)L∞(Ω) as t→∞t→∞.