The aim of this paper is to study the long-time dynamics of solutions of the evolution system
{utt− Δ u+ u+ η (− Δ) 1 2 u t+ a ϵ (t)(− Δ) 1 2 vt= f (u),(x, t)∈ Ω×(τ,∞), vtt− Δ v+ η (− Δ) 1 2 vt−
a ϵ (t)(− Δ) 1 2 ut= 0,(x, t)∈ Ω×(τ,∞), subject to boundary conditions u= v= 0,(x, t)∈∂
Ω×(τ,∞), where Ω is a bounded smooth domain in R n, n≥ 3, with the boundary∂ Ω
assumed to be regular enough, η> 0 is constant, a ϵ is a Hölder continuous function and f is
a dissipative nonlinearity. This problem is a non-autonomous version of the well known …

The aim of this paper is to study the long-time dynamics of solutions of the evolution
system\[\begin {cases} u_ {tt}-\Delta u+ u+\eta (-\Delta)^{\frac {1}{2}} u_t+ a_ {\epsilon}(t)(-
\Delta)^{\frac {1}{2}} v_t= f (u), &\;(x, t)\in\Omega\times (\tau,\infty),\\v_ {tt}-\Delta v+\eta (-
\Delta)^{\frac {1}{2}} v_t-a_ {\epsilon}(t)(-\Delta)^{\frac {1}{2}} u_t= 0, &\;(x, t)\in\Omega\times
(\tau,\infty),\end {cases}\] subject to boundary conditions\[u= v= 0,\;\;(x, t)\in\partial\Omega\
times (\tau,\infty),\] where $\Omega $ is a bounded smooth domain in $\mathbb {R}^ n …