Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application

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$ L^p $-$ L^q $ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data (2017, background): “Based on the linear estimates (3), many mathematicians studied the global existence and the blow-up of solutions (see [9, 10, 11, 12, 13, 15, 16, 18, 19, 20, 21, 22, 23, 24, 27, 30, 34, 36, 37] and the references therein).”
The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case (2020, background): “equation and the linear viscoelastic damped wave equation (or the strongly damped wave equation). This approximate relation is strongly related to the so-called diﬀusion phenomenon (see, for example, [45]), which bridges a connection for the damped wave equation and the heat equation such that τu”
L 1 Estimates for Oscillating Integrals Related to Structural Damped Wave Models (2013, background): “In both cases Lp−Lq estimates for the solutions are well understood; see [4–7, 10] and [11] for the case σ = 0 (linear or semi-linear models) and [8] for the case σ = 1.”
Weighted L2-estimates for dissipative wave equations with variable coefficients (2009, result): “This approach can generalize not only Matsumura’s estimates [M1] but also the more precise estimates in [NT2], [ NK2 ] for a = 1 and Strichartz’s estimates [SR] for a = 0.”