A quasilinear attraction–repulsion chemotaxis system of parabolic–elliptic type with logistic source
A quasilinear attraction–repulsion chemotaxis system of parabolic–elliptic type with logistic source
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DOI：
10.1016/j.jmaa.2016.03.061
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发表时间：
2016-09
影响因子：
1.3
通讯作者：
Yilong Wang
中科院分区：
文献类型：
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作者：
Yilong Wang
研究了具有Logistic源的拟线性抛物型椭圆型吸引-排斥趋化系统{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，在具有光滑边界的有界域Ω⊂Rn(n≥2)上的齐次Neumann边界条件下，其中D(U)≥c D(u+σ)m−1具有m≥1，σ≥0和c D>；0，f(U)≤a−b uη具有≥0，b>；0和η>；1.在非退化扩散(即σ>；在ξγ−χα>；0或Logistic阻尼足够强或扩散足够强的意义下，我们证明了系统存在唯一的全局有界经典解，而在退化扩散的情况下(即σ=0)，我们证明了系统至少在相同的假设下存在全局有界弱解。最后，我们得到了特定物流来源的解的大时间性态。
This study considers the following quasilinear attraction–repulsion chemotaxis system of parabolic–elliptic type with logistic source {u t=∇⋅(D (u)∇ u)−∇⋅(χ u∇ v)+∇⋅(ξ u∇ w)+ f (u), x∈ Ω, t> 0, 0= Δ v+ α u− β v, x∈ Ω, t> 0, 0= Δ w+ γ u− δ w, x∈ Ω, t> 0, under homogeneous Neumann boundary conditions in a bounded domain Ω⊂ R n (n≥ 2) with smooth boundary, where D (u)≥ c D (u+ σ) m− 1 with m≥ 1, σ≥ 0, and c D> 0, and f (u)≤ a− b u η with a≥ 0, b> 0, and η> 1. In the case of non-degenerate diffusion (ie, σ> 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 ξ γ− χ α> 0, or the logistic dampening is sufficiently strong, or the diffusion is sufficiently strong, while in the case of degenerate diffusion (ie, σ= 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.