Existence Of The Attractor For The Two Type Of Suspension Bridge Equations

In this master thesis,by using the theory of the infinite dimensional dynamical systems and the operator semigroup,we study the long time behavior of the nonau-tonomous suspension bridge equation with delay,and the coupled suspension bridge equation with linear memory,respectively.In the first part,we discuss long-time the behavior of the nonautonomous sus-pension bridge equation with delay.Firstly,we obtain the possedness corresponding the problem by using the theory of operator semigroup,then making use of the ener-gy functional we prove the existence of the uniformly bounded absorbing sets for a family of process {Ug(t,?)}t??in H,finally,we get the asymptotically compactness in the space H and obtain the uniform attractor for the process{Ug(t,?)}t??.In the second part,we study the asymptotic behavior of the coupled suspension bridge with linear memory,Firstly,we get the dissipativity of the system(H,s(t)),namely,it has a bounded absorbing set;Secondly,we prove the asymptotically compactness by the difference of two solutions,then we obtain the existence of the global attactor.