Article ID Journal Published Year Pages File Type
4614250 Journal of Mathematical Analysis and Applications 2016 34 Pages PDF
Abstract

This study considers the following quasilinear attraction–repulsion chemotaxis system of parabolic–elliptic type with logistic source{ut=∇⋅(D(u)∇u)−∇⋅(χu∇v)+∇⋅(ξu∇w)+f(u),x∈Ω,t>0,0=Δv+αu−βv,x∈Ω,t>0,0=Δw+γu−δw,x∈Ω,t>0, under homogeneous Neumann boundary conditions in a bounded domain Ω⊂Rn (n≥2)Ω⊂Rn (n≥2) with smooth boundary, where D(u)≥cD(u+σ)m−1D(u)≥cD(u+σ)m−1 with m≥1m≥1, σ≥0σ≥0, and cD>0cD>0, and f(u)≤a−buηf(u)≤a−buη with a≥0a≥0, b>0b>0, and η>1η>1. In the case of non-degenerate diffusion (i.e., σ>0σ>0), we show that the system admits a unique global bounded classical solution provided that the repulsion prevails over the attraction in the sense that ξγ−χα>0ξγ−χα>0, or the logistic dampening is sufficiently strong, or the diffusion is sufficiently strong, while in the case of degenerate diffusion (i.e., σ=0σ=0), we show that the system admits a global bounded weak solution at least under the same assumptions. Finally, we obtain the large-time behavior of solutions for a specific logistic source.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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