Long Time Behaviour Of The Type Of Kirchhoff Equation With Strong Damping

In this paper,we consider the initial boundary vale problem of the non-degenerate Kirchhoff equation with strong damping where M(s)= 1+sm/2,m≥1.Ω(?)RN is a bounded domain with smooth boundary (?)Ω.The paper using two different methods to prove that the above mentioned dynamical system possesses a global attractor which has finite Hausdorff dimension. 1.when m≥2, global attractor (?) has finite Hausdorff dimension. 2. when m≥1,by using the method of L-trajectories,it proves that the corresponding infinite dimensional dynamical system possesses a global attractor(?) which has finite Hausdorff dimension.Furfhermore,it proves that the above mentioned dynamical system possesses a exponential attractor M.