The Asymptotic Behavior Of Evolution Equation With Weak Dissipation And Memory

In this paper, we considered the existence and regularity of attractors, using the infinite dimensional system theory and semigroup theory, also studied the nonlinear evolution equations corresponding to the dynamic system behavior for a long time. The main work are as follows:i) We prove the existence of global attractor of the dissipative abstract evolution equations where the parameter θ∈(0,2], k(0), k(∞)>0, and k’(s)<0,(?)s∈R+. By adopting the method of defining functional,The existence of global attractor on the equations is obtained.Enrich the proofs of the existence of global attractor in the equation. At the same time, we obtain the regularity of the attractors, that is the existence of strong global attractors.ii) We prove the existence of global attractor of the weak dissipative memory type suspension bridge equations where f∈L2(Ω), σSaid elastic coefficient. When ignore the viscous damping item, Using the theory of semigroups in space V×H×Z2μ(R; V), The existence of global attractor on the equations is obtained conclusion, improved and promoted the equa-tions of the existence of global attractor in the already results.