Qualitative Analysis Of A Parabolic-elliptic Attraction-repulsion Chemotaxis Model

This paper deals with the parabolic-elliptic attraction-repulsion chemotaxis system t = Δu-(?)·(χu(?)v)+(?)·(ξμ(?)w),x ∈Ω,t>0,0 = Δv+αu-βv,x∈Ω,t>0,wt = Δw + γu-δw,x ∈Ω,t>0,under homogeneous Neumann boundary conditions where Ω is a bounded domain in R2 with smooth boundary(?)Ω,χ>0,ξ>0,α>0,γ>0,δ>0.By establishing appropriate entropy inequality and employing Lp-estimate method,the generalized Gagliardo-Nirenberg inequality and the Moser iteration technique,we prove that the model possesses a unique global solution provided the initial cell mass satisfies the condition that ‖u0‖L1(Ω)≤4/χαCNG.