The Dynamical Asymptotic Theory For The Suspension Bridge Equation

In this paper, we have great interest in the dissipative suspensionbridge equation:This paper is concerned with the asymptotic theory of this dynamical system.In the second chapter, the suspension bridge equation on unbounded domainR1 is considered. Applying with the method of decomposing operator and thetheory of constructing some compact operator in weighted space, the existenceof global attractor is obtained. In the third chapter, the suspension bridgeequation with the free initial boundary value condition is considered. The linearand nonlinear approximate inertial manifolds are constructed. The orders ofapproximations of the manifolds to the global attractor are derived. In thefourth chapter, the non-autonomous suspension bridge equation is considered.Using the method of describing non-autonomous dynamical system by operatorfamilies with two parameters, the existence of the uniform attractor of thesystem and the estimate of the uniform attractor's Hausdor? dimension areobtained.