Finite-dimensional Attractors For The Membrane 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 Membrane equation with strong damping where,Ω(?)R3 is a bounded domain with smooth boundary (?)Ω, and the assumptions on nonlinear termφ, f and external force g will be specified later.Undering rather mild conditions on nonlinear termsφ, f(u), the paper using standard Galerkin approximation scheme to prove the existence and uniqueness of global solutions in the space [W2,P+1∩Lq+2]×L2 of the above mentioned problem. And by using the method of L-trajectories proves that the corresponding infinite dimensional dynamical system possesses a (W1, W-1)- weak global attractor A which has finite fractal dimension and a (W1; W-1)- weak exponential attractor C.