Pullback attractors and upper semicontinuity for non-autonomous extensible two-beams

Abstract

In this paper we study the long-time dynamics for non-autonomous extensible non-symmetric two-beams. The governing equations describe the equilibria of an elastically-coupled extensible two-beams system subject to damping terms and evenly compressive axial loads. 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 prove the existence of pullback attractors in the natural space energy. Finally, we prove the regularity of the family of pullback attractors and its upper semicontinuous with respect to the perturbed parameters.