The fully parabolic Keller-Segel system is considered in n-dimensional balls with n ≥ 2. Pointwise time-independent estimates are derived for arbitrary radially symmetric solutions. These are firstly used to assert that any radial classical solution which blows up in finite time possesses a uniquely determined blow-up profile which satisfies an associated pointwise upper inequality. Secondly, in conjunction with additional regularity features implied by a very weak but temporally and spatially global quasi-entropy property, these estimates are seen to ensure global extensibility of any such solution within a suitable framework of renormalized solutions.

中文翻译：

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完全抛物线型 Keller-Segel 系统中的爆破轮廓和爆破后寿命

在 n ≥ 2 的 n 维球中考虑完全抛物线 Keller-Segel 系统。为任意径向对称解导出与时间无关的点估计。这些首先用于断言任何在有限时间内爆炸的径向经典解都具有唯一确定的爆炸轮廓，该轮廓满足相关的逐点上不等式。其次，结合非常弱但在时间和空间上全局准熵属性所隐含的额外规律特征，这些估计被视为确保任何此类解决方案在重整化解决方案的合适框架内的全局可扩展性。