On convergence to equilibria for the Keller–Segel chemotaxis model

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How strong a logistic damping can prevent blow-up for the minimal Keller–Segel chemotaxis system? (2016, background): “curs [14, 34, 58]. While, for arbitrarily small µ > 0, only existence of global weak solutions to (1.1) is available [26] in convex 3-D domains. Other dynamical properties of (1.1) can be found in [6, 12, 17, 27, 45, 59]. Finally, we observe that enormous variants of (1.1) have been considered to”
Asymptotic dynamics of the one‐dimensional attraction–repulsion Keller–Segel model (2015, result): “U, S/ follows from the results of [14] directly.”
Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening (2014, background): “Accordingly, the literature contains only few results on large time behavior in chemotaxis systems with parabolic signal evolution, many of them concentrating either on cases when diffusion at spatial infinity enforces convergence to zero, or also on special solution classes such as self-similar sol”