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- W3038153377 abstract "We consider the following quasilinear Keller–Segel system on a ball , n ≥ 3, R >0, under homogeneous Neumann boundary conditions and nonnegative initial data. The source term g ( u ) is superlinear and of logistic type, that is, g ( u )= λ u − μ u k , k >1, μ >0, λ >0, and T m a x is the blow‐up time. The solution ( u , v ) may or may not blow‐up in finite time. Under suitable conditions on data, we prove that the function u , which blows up in L ∞ (Ω)‐norm, blows up also in L p (Ω)‐norm for some p >1. Moreover, a lower bound of the lifespan (or blow‐up time when it is finite) T m a x is derived. In addition, if a lower bound of T m a x is explicitly computable." @default.
- W3038153377 created "2020-07-10" @default.
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- W3038153377 date "2020-07-04" @default.
- W3038153377 modified "2023-09-26" @default.
- W3038153377 title "Finite time collapse in chemotaxis systems with logistic‐type superlinear source" @default.
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- W3038153377 doi "https://doi.org/10.1002/mma.6676" @default.
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