The Existence Of Attractors And Upper Semicontinuity For Nonlinear Suspension Bridge Equations And The Related Problem On The Unbounded Domains

In this paper, we devote the long-time behavior of two classes of nonlinear evolution equations on the unbounded domain.This paper is divided into three sections.In the first section, we introduce research background of the problems and recall some preliminaries used in the main part of the paper.In the second section, we study the global attractors for the suspension bridge equation in IR, we decompose the domain into bounded and unbounded parts. For the unbounded parts, we appeal to the idea of uniform estimates to show that the norm of solutions are less than ε when t is large enough. For the bounded parts, we again apply the sequentially compact to prove the property of asymptotic smoothness of solutions. Ultimately, we prove the existence of global attractors for the problem in H2(R)×L2(R).In the three section, we study the upper semicontinuity of uniform attrac-tor for the plate equation on unbounded domain with singularly oscillating external forces, we consider for p ∈ [0,1) and ε>0, the plate equation on RN(N≥5) with a singularly oscillating external force, together with equation formally corresponding to the limiting case ε= 0. Under suitable assumptions on the external force, the uniform boundedness of the related uniform attrac-tors Aε is established as well as the convergence of the attractor Aε of the first equation to the attractor A0 of the second one as ε→0+.