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 quasi-linear structural damped wave equation where is a bounded domain with smooth boundary （?）Ω, the nonlinear term is f（u） and g is external force. we suppose that the growth exponent of f is q : 1≤ g < ∞, we prove that the solution for the equation is of higher global regularity as In natural energy spaceε =（W2,p+1∩H01）×L2 the existence of finite-dimensional global and exponential attractors is established as . When p’≤p < pα , we establish the existence of（ε,ε-θ） global attractor （weak global attractor） and （ε,ε-α） exponential attractor （weak exponential attractor）, where ε_-θ=W^2-θ,p+1×L²,ε_-α=V_α×V_-α.