Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation

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Attractiveness of Constant States in Logistic-Type Keller–Segel Systems Involving Subquadratic Growth Restrictions (2020, background): “under the hypotheses that n ∈ {3, 4} and α < (7)6 (see [45]), or n ≥ 5 and α < 3 2 + 1 2(n−1) (see [40]); recent progress indicates that similar statements are actually available under themere assumptions that n ≥ 3, α = 2 and μ > 0 is sufficiently small [10] (cf.”
Dissipative Gradient Nonlinearities Prevent δ$\delta$ ‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models (2024, unknown): “167 so the condition in [54, (1.4), Theorem 1.1] is satisfied.”
Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption (2022, background): “Ω u(x, t)dx + u (see also [Fue21] for a recent improvement of [Win11]), but later in [Win18b] also in 3-dimensional domains (with 0 = ∆v − v + u and β < 76 ).”