In this paper,we investigate the asymptotic behavior of solutions for the following strongly damped wave equations with periodic boundary condition:utt+??-???ut-?u+??u?=f,x??,t>0.where ? is a bounded domain in R3.u?x,t?:?ŚR+ ? R,??(0,1],the strongly damped coefficient ? is a positive constant,nonlinear term ?:R?R satisfy some growth conditions.f:??R is the external force.The wave equation is supplemented with the initial conditions:u?x,0?=u0?x?,ut?x,0?=u1?x?,x??.The dynamical properties of the partial differential equations,such as asymptotical be-haviors of solutions and global attractors,are important for the study of diffusion systems,which influence the stability of nonlinear diffusion phenomena and provides the mathe-matical foundation for the study of nonlinear dynamical system.This paper we prove the existence of the global attractor for the above equations with a quite general strongly damped term ??-???ut,??(0,1].When the nonlinearity is subcritical case,we prove the existence of an exponential attractor of optimal regularity and the bound of the Hausdorff dimension and fractal dimension of the global attractor. |