Uniform attractors for non-autonomous plate equations with <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian perturbation and critical nonlinearities

Abstract

This paper is concerned with the long-time behavior for a class of non-autonomous plate equations with perturbation and strong damping of $ p $-Laplacian type \begin{document}$ u_{tt} + \Delta^2 u + a_{\epsilon}(t) u_t - \Delta_p u - \Delta u_t + f(u) = g(x,t), $\end{document} in bounded domain $ \Omega\subset \mathbb{R}^N $ with smooth boundary and critical nonlinear terms. The global existence of weak solution which generates a continuous process has been presented firstly, then the existence of strong and weak uniform attractors with non-compact external forces also derived. Moreover, the upper-semicontinuity of uniform attractors under small perturbations has also obtained by delicate estimate and contradiction argument.