Attractors for a plate equation with nonlocal nonlinearities

This paper contains results on well‐posedness, stability, and long‐time behavior of solutions to a class of plate models subject to damping and source terms given by the product of two nonlinear components [EQUATION1] where Ω is a bounded open set of Rn with smooth boundary, γ,ρ⩾0 and are nonlocal functions. The main result states that the dynamical system {S(t)}t⩾0 associated with this problem has a compact global attractor. In addition, in the limit case γ = 0, it is also shown that {S(t)}t⩾0 has a finite dimensional global attractor by using an approach on quasi‐stability because of Chueshov–Lasiecka (2010).