Attractors For The Suspension Bridge Equations

In this article,we study the long-time behavior for the dynamical svs-tems corresponding to weakly dissipative hyperbolic equation.the coupled suspension bridge equation and the suspension bridge equations based on condition(C),respectively.The main work are as follows:i)We prove the existence of global attractor of weakly dissipative hy-perbolic equation with fading memory in a strong topology space D(A)×H01(Ω)×Lμ2(R+;D(A)).WhereΩ (?)R3is a bounded domain with a smooth boundary (?)Ω. κ(0),κ(∞)>0,and whenii) We obtain the existence of uniform attractor of the non-autonomous coupled suspension bridge equation with the corresponding initial-boundary value conditions in a weak topology space D(A)×L2(Ω)×H01(Ω)×L2(Ω)and in a strong topology0space D(A2)×D(A)×D(A)×H01(Ω).Where κ denotes the spring constant of the ties, α,β>0are the flexural rigidity of the structure and coefficient of tensile strength of the cable,respectively, δ1,δ2>0are constants.iii) We study the existence of pullback attractor of the non-autonomous suspension bridge equation in the strong topological space D(A)×H02(Ω).where Q is a bounded domain of R2with a smooth boundary (?)Ω.μut represents the viscous damping,κ denotes the spring constant,ku+represents the restoring force.