Asymptotic Behavior Of Solutions For Several Classes Of Dissipative Evolutionary Equations

In this paper, we studied several classes of dissipative evolutionary equations by use of the theory of infinite dimensional dynamic system, it including non-autonomous 2D Navier-Stokes equation with nonlinear term, suspension bridge-type equation and the hyperbolic equation with fading memory. The asymptotic behavior of solutions was discussed by some techniques of energy estimation and the semi-group theory on the basis of some existing results, the existence and the upper semi-continuity of attractors in some related systems were proved.In the first section, with respect to the non-autonomous 2D Navier-Stokes equation, it including nonlinear term c|u|?u, whereby c>0,1/3???2. The verify of uniform absorbing set and the compactness of the process of solution were very hard because of the nonlinear term, and the forcing term only satisfied the normal con-dition instead of translation compact, so the difficult was taken by use of semigroup theory, compact embedding theorem and the techniques of energy estimation. thus the existence of uniform attractors in cl?H01????2{u?C0????2, div u=0} was shown.In the second section, in regard to the suspension bridge-type equation, the enhance flattening property about semigroup was verified, thereby the existence of exponential attractors for the suspension bridge-type equation in the topological space H²??? ?H₀¹???×L²??? was obtained.In the third section, as regards the hyperbolic equation with fading memory, the continuous dependence of the parameter a in damping term was verified, thereby the upper semi-continuity of the strong global attractors in topological space D?A?x V×L_?²?R⁺;D?A?? was obtained.