Diffusion phenomenon for second order linear evolution equations

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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.”
Diffusion phenomenon in Hilbert spaces and applications (2011, methodology): “The diffusion phenomenon offers a tool to tackle qualitative aspects regarding the asymptotic behavior of solutions to damped hyperbolic problems.”
Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption (2006, unknown): “Recently, the precise diffusive structure as t → ∞ of the damped wave equation has been investigated in Marcati and Nishihara [23], Nishihara [27,28], Hosono and Ogawa [13], Narazaki [25], Ikehata and Nishihara [18], etc.”
The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case (2020, methodology): “Motivated by [24, 28], we will use Hardy’s inequality associated with a new variable to overcome the difficulty.”