Long Time Behavior Of High-order Kirchhoff-type Equation With Nonlinear

In this paper,we investigate the global well-posedness and the longtime dynamics of solutions for the higher-order Kirchhoff-type equation with nonlinear term (?) where ? is a bounded domain of Rn(n ? 1)with a smooth boundary(?)?,f(x),u0(x),u1(x)is a known function,and f(x)is the external interference,nonlinear fuction?(s)?C1[0,?),g(u)?C2(R).The main results are that existence and uniqueness of the solution is proved by using priori estimate and Galerkin method,the existence of the global attractor,and estimation Hausdorff and fractal dimensions of the global attractor.On this basis,the squeezing property of the nonlinear semi-group associate with this equation and the existence of exponential attractors are proved,at last,the inertial manifolds are also established by using the method of graph change.