L^P-L^Q Estimates for Damped Wave Equations and their Applications to Semi-Linear Problem

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Weighted L2-estimates for dissipative wave equations with variable coefficients (2009, background): “In the former case, u(t,x) C0w(t,x) with C0 depending on the initial data and w being a solution of the diusion equation wt w = 0, x 2 Rn, t > 0. More details are given in [ NT1 ].”
Damped wave equation with a critical nonlinearity (2005, methodology): “For the case of higher dimensions 4 ≤ n ≤ 5, global existence and L - time decay estimates for ρ ≤ q ≤ ρ ρ−1 were obtained via Fourier analysis in paper [12] (see Theorem 1.”
Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption (2006, unknown): “36) (see Matsumura [24] and [13,23,25,27]).”
Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption (2006, background): “See also Marcati and Nishihara [23] in 1-dimensional space, Hosono and Ogawa [15] in 2-dimensional space and Narazaki [25] in general space dimension and Ikehata [16], Ikehata and Nishihara [19], Chill and Haraux [3] in the abstract setting.”