The Existence Of Exponential Attractors For The One-Dimensional Suspension Bridge Equations

In this master's dissertation,we mainly consider the long time behavior of the one-dimensional suspension bridge equations.We apply the theories of infinite di-mensional dynamical systems,as well as the operator decomposition techniques to obtain our main results.The concrete contents are as follows:In the first part,we present,the ba.ckground and development of the suspension bridge equation.And then,we give our main problems which will be studied in this thesis.In the second part,we iterate some basic concepts about the infinite dimension-al dynamical systems and the abstract results of exponential attractors which are prepared for the follow-up work.In the third part,the existence of exponential attractors are shown for strong damped Kirchhoff-type suspension bridge equations.First,we obtain the existence of bounded absorbing sets in the L2(?)×H2(?)?H01(?)and H3×H1(?)by using the skill of energy estimate.Second,we prove the existence of exponential attractors.In the fourth part,we investigate the existence of exponential attractors for the damped suspension bridge equation with linear memory.Due to the equation in-cludes the memory term,they bring some difficulties in verifying the compactness of semigroup.Ultimately,after more complex and careful estimates,we abain the ex-istence of exponential attractors by the operator decomposing technique combining ·with the tail estimates of the memory term.