Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation
Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation
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DOI：
10.1007/s00033-018-0935-8
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发表时间：
2018-03
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影响因子：
--
通讯作者：
M. Winkler
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文献类型：
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作者：
M. Winkler
我们考虑 Keller-Segel 系统的径向对称解，广义逻辑源由 $$\begin{aligned} \left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v) + \lambda u - \mu u^\kappa , \\ 0 = \Delta v - v + u，\end{array} \right。 \qquad \qquad (\star ) \end{对齐}$$ u t = Δ u - ∇ · ( u ∇ v ) + λ u - μ u κ , 0 = Δ v - v + u , ( ⋆ ) 在齐次诺依曼球边界条件下Ω = B R ( 0 ) ⊂ R n forn ≥ 3 andR > 0 ，其中λ ∈ R , μ > 0 且κ > 1 。假设 $$\begin{aligned} \kappa < \left\{ \begin{array}{ll} \frac{7}{6} &{}\quad \text {if } n\in \{3,4\}, \\ 1+ \frac{1}{2(n-1)} &{}\quad \text {if } n \ge 5, \end{array} \right。 \end{对齐}$$ κ < ...
We consider radially symmetric solutions of the Keller–Segel system with generalized logistic source given by $$\begin{aligned} \left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v) + \lambda u - \mu u^\kappa , \\ 0 = \Delta v - v + u, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$ u t = Δ u - ∇ · ( u ∇ v ) + λ u - μ u κ , 0 = Δ v - v + u , ( ⋆ ) under homogeneous Neumann boundary conditions in the ballΩ = B R ( 0 ) ⊂ R n forn ≥ 3 andR > 0 , whereλ ∈ R , μ > 0 andκ > 1 . Under the assumption that $$\begin{aligned} \kappa < \left\{ \begin{array}{ll} \frac{7}{6} &{}\quad \text {if } n\in \{3,4\}, \\ 1+ \frac{1}{2(n-1)} &{}\quad \text {if } n \ge 5, \end{array} \right. \end{aligned}$$ κ < …