The threshold of effective damping for semilinear wave equations

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A classification of structural dissipations for evolution operators (2016, background): “t/ 2 Œ1,1/ is more delicate (see [5, 6]), whereas for limt!1 tb.”
Life-span of semilinear wave equations with scale-invariant damping: Critical Strauss exponent case (2017, background): “However, combing the result of [2] and [13], there is still gaps.”
Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data (2017, methodology): “On the one hand, global existence of small solutions (SDGE) is obtained for the following cases in [3]: ⎧ ⎪⎨ ⎪⎩ pF (1) < p < ∞ for N = 1, μ ≥ (5)3 , pF (2) < p < ∞ for N = 2, μ ≥ 3, pF (N ) < p ≤ N N−2 for N ≥ 3, μ ≥ N + 2.”