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- W2022885461 abstract "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." @default.
- W2022885461 created "2016-06-24" @default.
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- W2022885461 date "2015-02-01" @default.
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- W2022885461 title "Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source" @default.
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- W2022885461 doi "https://doi.org/10.1016/j.jde.2014.10.016" @default.
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