Asymptotic Behavior Of Solutions For Suspension Bridge Equations With Time Delay Modeled By Plate And Beam-string Coupled Equations With Nonlocal Damping

We mainly study the long-time dynamic behavior of solutions for non-autonomous suspension bridge equations with time delay modeled by plate and beam-string cou-pled system with nonlocal damping in this master's degree thesis.In the first part of this thesis,we consider the existence of uniform attractor for non-autonomous suspension bridge equations with nonlinear damping and time delay modeled by plate.Firstly,we prove the well-posedness of the solutions by using the theory of semigroup operator.Secondly,the existence of uniformly bounded absorbing sets for process family {U?(t,?)}(???)is obtained by constructing Lyapunov function,and further we prove that the process family {U?(t,?)}(???)is uniformly asymptotically compact.Finally,the existence of uniform attractor for this equations is obtained.In the second part,we consider the asymptotic behavior of solutions for coupled suspension bridge equations with nonlocal damping and nonlocal nonlinear terms.Firstly,we obtain the well-posedness of solutions by means of the monotone opera-tor theory,and then the existence of bounded absorbing sets of solution semigroup{s(t)}t?0 is proved.Next,we acquire the asymptotic smoothness of solution semi-groups {S(t)}t?0 by the energy reconstruction method,and the existence of global attractors is gained.Finally,we prove the existence of generalized exponential at-tractor for this equations.