Asymptotic behavior for the Kirchhoff type plate equation with nonlocal nonlinear damping

The current paper is devoted to the existence and regularity of a global attractor for a Kirchoff type plate equation with nonlocal nonlinear damping $ u_{tt}+\triangle^2u+\delta(\|\nabla u\|^2)\psi(u_t)+(\rho-\alpha\int_\Omega|\nabla u |^2 {{{\rm{d}}}} x)\triangle u+\varphi(u) = h(x) $. We establish that when the growth exponent $ p $ of the nonlinearity $ \varphi(u) $ satisfies $ 2\leq p\leq p^* $, the problem is well-posed and the related solution semigroup still has a global attractor in the natural energy space $ \mathcal{H} = H^2(\Omega)\cap H_0^1(\Omega)\times L^2(\Omega) $, where $ p^* = \frac{10q}{q+1}(\geq5) $ is a new exponent depending on $ q\in[1,9) $ which is the growth index of the nonlinear damping term $ \psi(u_t) $. Finally, by decomposing the weak solutions into two parts and conducting elaborate calculations, we derive the regularity of the global attractors.