The blow-up rate for semilinear parabolic problems on general domains

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Singularity and decay estimates in superlinear problems via liouville-type theorems. Part II: Parabolic equations (2007, background): “…t) −1/(p−1) , x ∈ Ω, 0 t T. (4.4) Indeed, estimate (4.4) with C depending on the solution u was known before for f (u) = u p , p p S , and for all blowing-up positive solutions, but under the assumption that Ω is convex [17] [18], or in general domains, but only for p ≤ (n + 3)/(n + 1) [11].”