On the global existence of solutions to an aggregation model

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Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity (2011, result): “p solutions were constructed if S(u) ≥ cu2n+ε for u > 1 with c > 0 and ε > 0, and if some further technical restrictions hold. As to the special case when S(u) = u, Kowalczyk and Szyman´ska ([KSz]) proved that solutions remain bounded under the condition that D(u) ≥ cu2− 4n+ε for all u >”
Boundedness of the attraction–repulsion Keller–Segel system (2015, unknown): “(See [14].”
Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system (2011, unknown): “[32], [22], [23], [24], [9], [4], [19], [33] and also the survey [16]).”
A critical blow-up exponent in a chemotaxis system with nonlinear signal production (2018, result): “which allows for a rather comprehensive knowledge with regard to the occurrence of blow-up: As already anticipated by some early partial results (see [41], [28] and [25], and also [10]) namely, if the positive parameter functions D and S in (1.”