Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics
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DOI：
10.1512/iumj.2016.65.5776
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发表时间：
2016
影响因子：
1.1
通讯作者：
M. Winkler;Xueli Bai
中科院分区：
文献类型：
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作者：
M. Winkler;Xueli Bai
在具有光滑边界的有界区域Ω <$R中考虑了。证明了当n ≤ 2且（n）中的参数仅为正时，对任意适当正则的非负初值u 0，v0和w 0，相应的Neumann初边值问题存在唯一的整体有界解.通过构造适当的能量泛函，证明了：当n ≥ 1时，·如果a1 < 1，a2 < 1，μ1和μ2都充分大，则任何由满足u 0 6 <$0 6 <$v0的充分正则初值所产生的全局有界解满足（u，v，w）（·，t）→当t → ∞时，（u，v，w）在Ω中一致，其中（u，v，w）表示（u）的唯一正空间齐次平衡点，并且如果a1 ≥ 1且a2 < 1且μ2足够大，则所有具有合理光滑初始数据且满足v 0 6 <$0的整体有界解具有以下性质：
is considered in a bounded domain Ω ⊂ R with smooth boundary. It is shown that if n ≤ 2 and all parameters in (⋆) are merely positive, then for all appropriately regular nonnegative initial data u0, v0 and w0 the corresponding Neumann initial-boundary value problem possesses a unique global bounded solution. Moreover, by means of the construction of suitable energy functionals it is proved that whenever n ≥ 1, • if a1 < 1 and a2 < 1 and both μ1 and μ2 are sufficiently large, then any global bounded solution emanating from adequately regular initial data fulfilling u0 6≡ 0 6≡ v0 satisfies (u, v, w)(·, t) → (u⋆, v⋆, w⋆) uniformly in Ω as t → ∞, where (u⋆, v⋆, w⋆) denotes the unique positive spatially homogeneous equilibrium of (⋆), and that • if a1 ≥ 1 and a2 < 1 and μ2 is large enough, then all global bounded solution with reasonably smooth initial data satisfying v0 6≡ 0 have the property that