Robust attractors for a Kirchhoff-Boussinesq type equation

The paper studies the existence of the pullback attractors and robust pullback exponential attractors for a Kirchhoff-Boussinesq type equation: $ u_{tt}-\Delta u_{t}+\Delta^{2} u = div\Big\{\frac{\nabla u}{\sqrt{1+|\nabla u|^{2}}}\Big\}+\Delta g(u)+f(x,t) $. We show that when the growth exponent $ p $ of the nonlinearity $ g(u) $ is up to the critical range: $ 1\leq p\leq p^*\equiv\frac{N+2}{(N-2)^{+}} $, (ⅰ) the IBVP of the equation is well-posed, and its solution has additionally global regularity when $ t>\tau $; (ⅱ) the related dynamical process $ \{U_f(t,\tau)\} $ has a pullback attractor; (ⅲ) in particular, when $ 1\leq p< p^* $, the process $ \{U_f(t,\tau)\} $ has a family of pullback exponential attractors, which is stable with respect to the perturbation $ f\in \Sigma $ (the sign space).