Stabilization for small mass in a quasilinear parabolic--elliptic--elliptic attraction-repulsion chemotaxis system with density-dependent sensitivity: repulsion-dominant case
Stabilization for small mass in a quasilinear parabolic--elliptic--elliptic attraction-repulsion chemotaxis system with density-dependent sensitivity: repulsion-dominant case
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发表时间：
2022-03
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通讯作者：
Yutaro Chiyo
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作者：
Yutaro Chiyo
。本文研究了具有光滑边界 ∂ Ω 的有界域 Ω ⊂ R n ( n ∈ N ) 中的拟线性吸引-排斥趋化系统 − δw，其中 m、p、q ∈ R 、χ、ψ、α、β、γ、δ > 0 是常数。在 m = 1 且 p = q = 2 的情况下，当 χα − ψγ < 0 且 β = δ 时，Tao-Wang (Math. Models Method Appl. Sci.; 2013; 23; 1-36) 通过将 Keller-Segel 系统简化为以下公式，证明了朝向空间常数平衡 ( u 0 , α β u 0 , γδ u 0 ) 的全局有界经典解：使用变换 z := χv − ψw ，其中 u 0 是初始数据 u 0 的空间平均值。然而，由于上述系统涉及非线性，该方法不再有效。本文的目的是建立全局有界经典解收敛于空间常数平衡 ( u 0 , αβ 0 , γ δ u
. This paper deals with the quasilinear attraction-repulsion chemotaxis system − δw in a bounded domain Ω ⊂ R n ( n ∈ N ) with smooth boundary ∂ Ω, where m, p, q ∈ R , χ, ξ, α, β, γ, δ > 0 are constants. In the case that m = 1 and p = q = 2, when χα − ξγ < 0 and β = δ , Tao–Wang (Math. Models Methods Appl. Sci.; 2013; 23; 1–36) proved that global bounded classical solutions toward the spatially constant equilibrium ( u 0 , α β u 0 , γδ u 0 ) via the reduction to the Keller–Segel system by using the transformation z := χv − ξw , where u 0 is the spatial average of the initial data u 0 . However, since the above system involves nonlinearities, the method is no longer valid. The purpose of this paper is to establish that global bounded classical solutions converge to the spatially constant equilibrium ( u 0 , αβ 0 , γ δ u