Blowup and global solutions in a chemotaxis–growth system

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Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation (2018, background): “The few available exceptions address the taxis-driven spontaneous emergence of arbitrarily large population densities, possibly in the form of transient phenomena, in presence of suitably small diffusion and death parameters even in spatially one-dimensional, but also in higher-dimensional Keller-Se”
Attractiveness of Constant States in Logistic-Type Keller–Segel Systems Involving Subquadratic Growth Restrictions (2020, background): “Besides providing numerical evidence that shows remarkably colorful facets in logistic Keller–Segel systems, up to even chaotic behavior [28], previous studies have revealed quite drastic phenomena related to the spontaneous emergence of large population densities, possibly at intermediate timescale”
Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion (2019, methodology): “The boundedness and global existence of Tello-Winkler were first extended for (1.6) to the borderline case by Kang and Stevens [11] under χ = 1, θ = 2, κ = 1, n ≥ 3, b ≥ b∗ := (n− 2) n .”