Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent

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Asymptotic regularity for some dissipative equations (2010, background): “Now, similarly as in Zelik [33], based on Lemmas 4.2 and 4.3 we can decompose u(t) as follows.”
Smooth attractors for strongly damped wave equations (2006, background): “The proof is more complicated, and it requires a different splitting of u along with an ad hoc argument, devised in [20], and the transitivity property of exponential attraction, introduced and proved in [8].”
Fractal dimension of random attractor for stochastic non-autonomous damped wave equation with linear multiplicative white noise (2015, methodology): “It is worth mentioning that we need to prove the higher regularity of random attractor by a recurrence method, for this aim, we establish some new argument basing on the idea of [31].”
Dynamics of strongly damped wave equations in locally uniform spaces: Attractors and asymptotic regularity (2008, methodology): “P. Fabrie, C. Galushinski, A. Miranville and S. Zelik, Uniform exponential attractors for a singular perturbed damped wave equation, Discrete Contin.”