Finite-dimensional Attractors For The Wave Model Equation With Damping Term

In this paper, we are concerned with the existence of the finite-dimensional global attractor and exponential attractor for the wave equation with damping term where Ω(?) R3is a bounded domain with smooth boundary δΩ. and the assumptions on nonlinear term f(υ) and external force g will be specified later.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 Y=Y(q)=[H1(Ω))∩Lq+1(Ω)]×L2(Ω) of the above mentioned problem. And by using the method of L-trajectories proves that the corresponding infinite dimensional dynamical system possesses a (Yq,Y-1)-weak global attractor A which has finite fractal dimension and a (Yq, Y-1)-weak exponential attractor M.