A critical blow-up exponent in a chemotaxis system with nonlinear signal production

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Dissipative Gradient Nonlinearities Prevent δ$\delta$ ‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models (2024, unknown): “Conversely, for α > 2 n , blow-up phenomena may occur (refer to [53] for further details).”
Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption (2022, background): “Conversely, for a further simplification of the parabolic-elliptic formulation, in spatially radial contexts it is known (see [36]) that the value 2 n is critical, in the sense that the boundedness of solutions is guaranteed for any n ≥ 1 and 0 < k < 2 n , whereas for k > 2 n blow-up phenomena may o”