A Modified Test Function Method for Damped Wave Equations

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The threshold of effective damping for semilinear wave equations (2015, background): “More precisely, for suitable, arbitrarily small data, there exists no global weak solution to (1) if p 1C 2=n and 1 [13].”
Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation (2017, methodology): “It was recently shown in [4], [5] that when μ1 ≥ (5)3 if n = 1, μ1 ≥ 3 if n = 2 and μ1 ≥ n + 2 if n ≥ 3, then pFu j (n) is the critical exponent as in the general case with effective dissipation [7].”