Existence and uniform decay for a non‐linear viscoelastic equation with strong damping

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Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity (2019, unknown): “[7] studied, in a bounded domain, the following equation: |ut|utt −∆u−∆utt + ∫ t”
General decay of solutions of a nonlinear system of viscoelastic wave equations (2011, methodology): “Our approach here allows us to weaken some of the technical assumptions of [6,7], for convolution kernels.”
Global existence and uniform stability of solutions for a quasilinear viscoelastic problem (2007, background): “This type of equations usually appears as a model in nonlinear viscoelasticity (see [1]).”
Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping. (2004, unknown): “Introduction Cavalcanti et al [3] studied the equation utt −∆u + ∫ t 0 g(t− τ)∆u(τ)dτ + a(x)ut + |u|γu = 0, in Ω× (0,∞) u(x, t) = 0, x ∈ ∂Ω, t ≥ 0 u(x, 0) = u0(x), ut(x, 0) = u1(x), x ∈ Ω, (1.1) where Ω is a bounded domain of Rn (n ≥ 1) with a smooth boundary ∂Ω, γ > 0, g is a positive function, and”