Long-time behavior for a plate equation with nonlocal weak damping

This paper is devoted to the long-time behavior of solutions for a class of plate equations with nonlocal weak damping uₜₜ + Δ² u + g(u) + M (∫Ω|∇ u|² dx )uₜ =f in Ω⁺, where Ω is a bounded domain of RN. Under suitable conditions on the nonlinear forcing term $g(u)$ and Kirchhoff damping coefficient M (∫|∇ u|² ), the existence of a global attractor with finite Hausdorff and fractal dimensions is proved.