Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source
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DOI：
10.1016/j.jde.2014.10.016
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发表时间：
2014-07
影响因子：
2.4
通讯作者：
J. Lankeit
中科院分区：
文献类型：
--
作者：
J. Lankeit
证明了光滑有界凸区域Ω <$Rn中，在齐次Neumann边界条件下，趋化性系统ut = Δ u− ε v（u ε v）+ κ u− μ u 2 v t= Δ v− v+ u的整体弱解的存在性，对于任意小的μ> 0.此外，我们表明，在三维设置，经过一段时间后，这些解决方案成为经典的解决方案，提供的κ不是太大。在这种情况下，我们也考虑了它们的大时间行为：我们证明了当κ≤ 0时的衰变和当κ> 0足够小时的吸收集的存在。
We prove existence of global weak solutions to the chemotaxis system u t= Δ u−∇⋅(u∇ v)+ κ u− μ u 2 v t= Δ v− v+ u under homogeneous Neumann boundary conditions in a smooth bounded convex domain Ω⊂ R n, for arbitrarily small values of μ> 0. Additionally, we show that in the three-dimensional setting, after some time, these solutions become classical solutions, provided that κ is not too large. In this case, we also consider their large-time behaviour: We prove decay if κ≤ 0 and the existence of an absorbing set if κ> 0 is sufficiently small.