Large time behavior and Lp−Lq estimate of solutions of 2-dimensional nonlinear damped wave equations

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Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (2007, background): “A huge amount of work has been done during many years around the special case of the dissipative (nonlinear) wave equation, see for instance [14, 24, 29] and references therein.”
Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption (2006, background): “36) (see Matsumura [24] and [13,23,25,27]).”
$ L^p $-$ L^q $ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data (2017, background): “xistence of the global solution with small data even for the critical nonlinearity. Based on the linear estimates (1.3), many mathematicians studied the global existence and 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 there”
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.”