Global Existence and Aggregation in a Keller–Segel Model with Fokker–Planck Diffusion

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Logistic damping effect in chemotaxis models with density-suppressed motility (2021, background): “However, γ(v) may not have priori positive lower/upper bound, for example, γ(v) = c0 vk , for which it was proved in [45] that global bounded solutions exist in all dimensions for any k > 0 provided that c0 > 0 is small.”
Delayed blow‐up for chemotaxis models with local sensing (2020, background): “We also mention the work [35] where smooth solutions are obtained in the two-dimensional case for a motility γ taken sufficiently small.”
Global existence and infinite time blow-up of classical solutions to chemotaxis systems of local sensing in higher dimensions (2021, unknown): “1) with some polynomial decaying function γ are obtained under smallness conditions on some parameters in [18, 3, 6].”