Long Time Behavior Of A Class Of Nonlinear High-order Coupled Kirchhoff-type Equations

In this thesis,we mainly deal with the well-posedness of solution,global attractor,ex-ponential attractor and the inertial manifold for a class of high-order coupled Kirchhoff-type equations with nonlinear strong damping terms and source terms.Under the appro-priate assumptions,the existence and uniqueness of the global solution of the equations are proved by means of prior estimates and Galerkin method,and then by applying the solution semigroup and constructing the bounded absorption set method,furthermore,the existence of global attractor of the equations is obtained.Based on the above work,the discrete squeezing property and Lipschitz property of nonlinear Semigroups related to the initial boundary value problem are proved.According to the proof of the above proper-ties,the existence of exponential attractor is obtained.Finally,the existence of inertial manifold is proved by organizing the original equations into the first-order evolution e-quation,constructing the corresponding graph norm and verifying the spectral interval condition.