Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation

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A competition between Fujita and Strauss type exponents for blow-up of semi-linear wave equations with scale-invariant damping and mass (2019, background): “ terms of µ 1 and µ2 2, the assumption that we require for our model in this paper. If we deﬁne δ:= (µ 1 −1)2 −4µ2 2, then our assumption for these coeﬃcients is δ∈ (0,1]. (1.2) As it is explained in [22], the quantity δdescribes in some sense the interplay between the damping and the mass term in (”
The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case (2020, background): “While in the estimate of the second norm, the main tools are the fractional Leibniz rule and the fractional chain rule (see [21] and [46]) carrying a stronger condition p > 1 + ⌈s − 2⌉ > 2.”