Asymptotic Behavior Of Solutions For The Non-autonomous Suspension Bridge

In this paper, we study the long-time behavior of the solutions for the non-autonomous suspension bridge equations. Recently, many mathematical authors are interested in them and have obtained some excellent results such as [1-6].Our main results:we consider the following non-autonomous suspension bridge equations where Ω is a bounded domain in R5with smooth boundary. First, when g E Lb2(R,H2(Ω)), we obtain the existence of uniform compact attractors in H0. Fur-thermore, the asymptotic regularity of solution is proved, and based on this regu-larity, we investigate the existence of the exponential attractors in H0for the case g∈Lb2(R,L2(Ω)).