Long Time Behavior Of A Class Of Nonlinear Generalized Kirchhoff-Boussinesq Equation

In this paper,we consider the long time behavior of solution of the initial boundary value problem of a class of nonlinear Generalized Kirchhoff-Boussinesq equation(?)where ?>0,?>0,??RN is a bounded domain with smooth boundary(?)?This paper presents the nonlinear terms g(??u?2?u)and h(u)two different assump-tions,by a priori estimates and Galerkin method,we get the existence and uniqueness of the global solution of the above problem;the compact method and the decomposition of strong solution method are used to prove the global attractor in the above problem;then the existence of exponential attractor is proved by discussing its squeezing properties;and the existence of inertial manifold in the above problem is proved by using spectral interval conditions.