Abstract
We consider the degenerate Keller-Segel system (KS) of Nagai type below. We prove that when $m > 2-\frac{2}{N}$, the problem (KS) is solvable globally in time without any restriction on the size of the initial data and that when $1 < m \le 2-\frac{2}{N}$, the problem (KS) evolves in a finite time blow-up for some large initial data. Hence, we completely classify the existence and non-existence of the time global solution by means of the exponent $m=2-\frac{2}{N}$, which generalizes the Fujita exponent for (KS).
Citation
Yoshie Sugiyama. "Global existence in sub-critical cases and finite time blow-up in super-critical cases to degenerate Keller-Segel systems." Differential Integral Equations 19 (8) 841 - 876, 2006. https://doi.org/10.57262/die/1356050338
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