Universal bounds at the blow-up time for nonlinear parabolic equations

By D. Andreucci, Anatoli F. Tedeev. Advances in Differential Equations, 2005

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Singularity and decay estimates in superlinear problems via liouville-type theorems. Part II: Parabolic equations (2007, background): “7) for p < (n + 2)/n is a consequence of [1] (see also [2, 3]).”
The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equations (2007, methodology): “Finally, in the proof of L1 L1 estimates we combine the local integral approaches of [16] and [2] with the one that has been proposed in [7].”
Qualitative properties of solutions to a time-space fractional evolution equation (2012, methodology): “For more informations, we refer the reader to the excellent paper of Andreucci and Tedeev [1] for the blow-up rate by an alternative method The organization of this paper is as follows.”
Well-posedness, global existence and large time behavior for Hardy–Hénon parabolic equations (2017, methodology): “On the hand, the following upper blow-up estimate has been established by [1, Theorems 1.2 and 1.3] and [7, Theorem 1.6] in the case q = ∞ (with various restriction on α ): Note that there is a gap between the above lower and upper estimates (1.8) and (1.9), in particular for solutions blowing up…”