Long-time Dynamics For A Class Of Nonlinear Wave Equations With Structural Damping

In this paper, we are concerned with the existence of global attractor and exponential attractor for the nonlinear wave equation with structural damping term where Ω∈RN is a bounded domain with smooth boundary (?)Ω, the nonlinear terms are f(u), and g is external force.Under the dissipativeness condition and the growth condition on nonlinear term, First, the paper uses the standard Galerkin approximation scheme to prove well-posedness global solutions for the above mentioned problem in the space ε(q)=[H01∩L9+2](Ω)×L2(Ω). and energy identity is valid. we prove the dynamical system associated with the above-mentioned equation possess a global attractor, we get exponential attractor by virtue of weak quasi-stability estimates.