Finite-dimensional Attractors For The Kirchhoff Model Equation With Strong Damping Term

In this paper, we are concerned with the existence of the finite-dimensional global attractor and exponential attractor for the Kirchhoff models equation with strong damping whereσ(s)= s(m-1)/2, s≥0, m≥1,Ω(?) RN is a bounded domain with smooth boundary (?)Ω, g(u) is nonlinear term and f is external force.Undering rather mild conditions on nonlinear terms, the paper using standard Galerkin approximation scheme to prove the existence and uniqueness of global solutions in the space X1= V2 x H of the above mentioned problem. And by using the method of L-tra.jectories proves that the corresponding infinite dimensional dynamical system possesses a (X1,X2)-weak global attractor A which has finite fractal dimension and a (X1, X2)-weak exponen-tial attractor M.