Stabilization and convergence rate in a chemotaxis system with consumption of chemoattractant
Stabilization and convergence rate in a chemotaxis system with consumption of chemoattractant
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DOI：
10.1063/1.4929658
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发表时间：
2015-08
影响因子：
1.3
通讯作者：
Qingshan Zhang;Yuxiang Li
中科院分区：
文献类型：
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作者：
Qingshan Zhang;Yuxiang Li
在齐次Neumann边界条件下，考虑具有趋化物质消耗的趋化系统{Vt=Δv−uv，ut=Δu−χ∇⋅(u∇v).证明了当n≤2或0<；χ≤16(n+1)‖v(x，0)‖∞(Ω)，n≥3时，该问题的整体经典解(u，v)以t→∞指数收敛到(u0，0)，其中u0≔1|Ω|∫Ωu(x，0)dx.
We consider chemotaxis system with consumption of chemoattractant {vt=Δv−uv,ut=Δu−χ∇⋅(u∇v), under homogeneous Neumann boundary conditions. It is proved that if either n ≤ 2 or 0<χ≤16(n+1)‖v(x,0)‖L∞(Ω), n ≥ 3, the global classical solution (u, v) of this problem converges to (u0,0) exponentially as t → ∞, where u0≔1|Ω|∫Ωu(x,0)dx.