Regularity and upper semicontinuity of pullback attractors for non-autonomous Rao–Nakra beam

Abstract

In this paper we study the long-time dynamics of a non-autonomous Rao–Nakra sandwich beam. The governing equations of Rao–Nakra sandwich beam consist of two wave equations for the longitudinal displacements of the top and bottom layers, and one Euler–Bernoulli beam equation for the transversal displacement. Under quite general assumptions on nonlinear damping and sources terms and based on nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions. We also establish a Lipschitz stability result. We prove the existence of pullback attractors in natural space energy. Finally, we prove the regularity of the family of pullback attractors and its upper semicontinuous with respect to the fractional exponent γ ∈ (0, 1/2).